let B be Boolean Lattice; :: thesis: ( ( for v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v0,v1) = v0 ) & ( for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,v0,v1) ) & ( for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v2,v1) ) & ( for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v1,v3) = Tern (v0,v1,(Tern (v2,v1,v3))) ) implies for v1, v2, v3, v4, v5 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v4,(Tern (v1,v2,v5))) = Tern (v1,v2,(Tern (v3,v4,v5))) )
assume A2: for v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v0,v1) = v0 ; :: thesis: ( ex v2, v1, v0 being Element of (BA2TBAA B) st not Tern (v0,v1,v2) = Tern (v2,v0,v1) or ex v2, v1, v0 being Element of (BA2TBAA B) st not Tern (v0,v1,v2) = Tern (v0,v2,v1) or ex v3, v2, v1, v0 being Element of (BA2TBAA B) st not Tern ((Tern (v0,v1,v2)),v1,v3) = Tern (v0,v1,(Tern (v2,v1,v3))) or for v1, v2, v3, v4, v5 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v4,(Tern (v1,v2,v5))) = Tern (v1,v2,(Tern (v3,v4,v5))) )
assume A3: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,v0,v1) ; :: thesis: ( ex v2, v1, v0 being Element of (BA2TBAA B) st not Tern (v0,v1,v2) = Tern (v0,v2,v1) or ex v3, v2, v1, v0 being Element of (BA2TBAA B) st not Tern ((Tern (v0,v1,v2)),v1,v3) = Tern (v0,v1,(Tern (v2,v1,v3))) or for v1, v2, v3, v4, v5 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v4,(Tern (v1,v2,v5))) = Tern (v1,v2,(Tern (v3,v4,v5))) )
assume A4: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v2,v1) ; :: thesis: ( ex v3, v2, v1, v0 being Element of (BA2TBAA B) st not Tern ((Tern (v0,v1,v2)),v1,v3) = Tern (v0,v1,(Tern (v2,v1,v3))) or for v1, v2, v3, v4, v5 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v4,(Tern (v1,v2,v5))) = Tern (v1,v2,(Tern (v3,v4,v5))) )
assume A5: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v1,v3) = Tern (v0,v1,(Tern (v2,v1,v3))) ; :: thesis: for v1, v2, v3, v4, v5 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v4,(Tern (v1,v2,v5))) = Tern (v1,v2,(Tern (v3,v4,v5)))
A7: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),v1) = Tern (v0,v1,(Tern (v2,v1,v3)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),v1) = Tern (v0,v1,(Tern (v2,v1,v3)))
Tern ((Tern (v0,v1,v2)),v1,v3) = Tern (v3,(Tern (v0,v1,v2)),v1) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),v1) = Tern (v0,v1,(Tern (v2,v1,v3))) by A5; :: thesis: verum
end;
A10: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v2,v0,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v3,v2,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v2,v0,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v3,v2,v0)))
Tern (v0,(Tern (v1,v2,v3)),v2) = Tern (v2,v0,(Tern (v1,v2,v3))) by A3;
hence Tern (v2,v0,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v3,v2,v0))) by A7; :: thesis: verum
end;
A13: for v1, v3, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v0,v3))) = Tern (v2,v0,(Tern (v0,v1,v3)))
proof
let v1, v3, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v0,v3))) = Tern (v2,v0,(Tern (v0,v1,v3)))
Tern (v0,v1,v3) = Tern (v3,v0,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v0,v3))) = Tern (v2,v0,(Tern (v0,v1,v3))) by A10; :: thesis: verum
end;
A15: for v1, v3, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v0,v3))) = Tern (v2,v0,(Tern (v0,v3,v1)))
proof
let v1, v3, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v0,v3))) = Tern (v2,v0,(Tern (v0,v3,v1)))
Tern (v0,v1,v3) = Tern (v0,v3,v1) by A4;
hence Tern (v0,v1,(Tern (v2,v0,v3))) = Tern (v2,v0,(Tern (v0,v3,v1))) by A13; :: thesis: verum
end;
A17: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v2,v0,(Tern (v0,v3,v1)))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v2,v0,(Tern (v0,v3,v1)))
Tern (v0,v3,v2) = Tern (v2,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v2,v0,(Tern (v0,v3,v1))) by A15; :: thesis: verum
end;
A20: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v3,v0,(Tern (v0,v2,v1)))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v3,v0,(Tern (v0,v2,v1)))
Tern (v0,v2,v3) = Tern (v0,v3,v2) by A4;
hence Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v3,v0,(Tern (v0,v2,v1))) by A17; :: thesis: verum
end;
A23: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v2,v0,(Tern (v0,v1,v3)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v2,v0,(Tern (v0,v1,v3)))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v2,v0,(Tern (v0,v1,v3))) by A20; :: thesis: verum
end;
A25: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,(Tern (v0,v1,v3)),v2)
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,(Tern (v0,v1,v3)),v2)
Tern (v0,(Tern (v0,v1,v3)),v2) = Tern (v2,v0,(Tern (v0,v1,v3))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,(Tern (v0,v1,v3)),v2) by A23; :: thesis: verum
end;
A27: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v0,v1,v3)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v0,v1,v3)))
Tern (v0,(Tern (v0,v1,v3)),v2) = Tern (v0,v2,(Tern (v0,v1,v3))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v0,v1,v3))) by A25; :: thesis: verum
end;
assume not for v1, v2, v3, v4, v5 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v4,(Tern (v1,v2,v5))) = Tern (v1,v2,(Tern (v3,v4,v5))) ; :: thesis: contradiction
then consider c1, c2, c3, c4, c5 being Element of (BA2TBAA B) such that
A28: not Tern ((Tern (c1,c2,c3)),c4,(Tern (c1,c2,c5))) = Tern (c1,c2,(Tern (c3,c4,c5))) ;
A30: not Tern (c4,(Tern (c1,c2,c5)),(Tern (c1,c2,c3))) = Tern (c1,c2,(Tern (c3,c4,c5))) by A3, A28;
A32: not Tern (c4,(Tern (c1,c2,c3)),(Tern (c1,c2,c5))) = Tern (c1,c2,(Tern (c3,c4,c5))) by A4, A30;
A34: for v0, v1 being Element of (BA2TBAA B) holds Tern (v1,v0,v0) = v0
proof
let v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v0,v0) = v0
Tern (v0,v0,v1) = Tern (v1,v0,v0) by A3;
hence Tern (v1,v0,v0) = v0 by A2; :: thesis: verum
end;
A38: for v100, v3, v2, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v2,v3)),v102) = Tern (v102,v2,(Tern (v102,v100,v3)))
proof
let v100, v3, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v2,v3)),v102) = Tern (v102,v2,(Tern (v102,v100,v3)))
Tern (v102,v100,(Tern (v102,v2,v3))) = Tern (v102,v2,(Tern (v102,v100,v3))) by A27;
hence Tern (v100,(Tern (v102,v2,v3)),v102) = Tern (v102,v2,(Tern (v102,v100,v3))) by A3; :: thesis: verum
end;
A41: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v1,v0,v3)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v1,v0,v3)))
Tern (v0,(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v1,v0,v3))) by A38; :: thesis: verum
end;
A43: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v3,v1)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v3,v1)))
Tern (v0,v3,v1) = Tern (v1,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v3,v1))) by A41; :: thesis: verum
end;
A45: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v1,v3)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v1,v3)))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v1,v3))) by A43; :: thesis: verum
end;
A49: for v1, v2, v0, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v0,v1,v3)))
proof
let v1, v2, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v0,v1,v3)))
Tern (v0,v2,v3) = Tern (v3,v0,v2) by A3;
hence Tern (v0,v1,(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v0,v1,v3))) by A27; :: thesis: verum
end;
A52: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v0,v3,(Tern (v0,v1,v2)))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v0,v3,(Tern (v0,v1,v2)))
Tern (v0,v3,v2) = Tern (v2,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v0,v3,(Tern (v0,v1,v2))) by A49; :: thesis: verum
end;
A55: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v0,v2,(Tern (v0,v1,v3)))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v0,v2,(Tern (v0,v1,v3)))
Tern (v0,v2,v3) = Tern (v0,v3,v2) by A4;
hence Tern (v0,v1,(Tern (v0,v3,v2))) = Tern (v0,v2,(Tern (v0,v1,v3))) by A52; :: thesis: verum
end;
A59: for v101, v2, v3, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v2,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,v3)))))
proof
let v101, v2, v3, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v2,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,v3)))))
Tern (v100,v102,(Tern (v100,v2,v3))) = Tern (v100,v2,(Tern (v100,v102,v3))) by A27;
hence Tern (v100,v101,(Tern (v100,v2,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,v3))))) by A27; :: thesis: verum
end;
A63: for v103, v101, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,v103) = Tern (v100,v103,(Tern (v100,v101,v103)))
proof
let v103, v101, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,v103) = Tern (v100,v103,(Tern (v100,v101,v103)))
Tern (v100,v103,v103) = v103 by A34;
hence Tern (v100,v101,v103) = Tern (v100,v103,(Tern (v100,v101,v103))) by A27; :: thesis: verum
end;
A69: for v103, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v102,v103) = Tern (v100,v102,(Tern (v100,(Tern (v100,v102,v103)),v103)))
proof
let v103, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v102,v103) = Tern (v100,v102,(Tern (v100,(Tern (v100,v102,v103)),v103)))
Tern (v100,(Tern (v100,v102,v103)),(Tern (v100,v102,v103))) = Tern (v100,v102,v103) by A34;
hence Tern (v100,v102,v103) = Tern (v100,v102,(Tern (v100,(Tern (v100,v102,v103)),v103))) by A27; :: thesis: verum
end;
A72: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v2)))))
proof
let v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v0,v1,v2)),v2) = Tern (v0,v2,(Tern (v0,v1,v2))) by A4;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v2))))) by A69; :: thesis: verum
end;
A74: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v1,v2)))
proof
let v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v1,v2)))
Tern (v0,v2,(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A63;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v1,v2))) by A72; :: thesis: verum
end;
A78: for v101, v102, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,v102)))))
proof
let v101, v102, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,v102)))))
Tern (v100,v102,(Tern (v100,v2,v102))) = Tern (v100,v2,v102) by A63;
hence Tern (v100,v101,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,v102))))) by A27; :: thesis: verum
end;
A84: for v102, v101, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v2,v101))))) = Tern (v100,v102,(Tern (v100,v2,v101)))
proof
let v102, v101, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v2,v101))))) = Tern (v100,v102,(Tern (v100,v2,v101)))
Tern (v100,v101,(Tern (v100,v2,v101))) = Tern (v100,v2,v101) by A63;
hence Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v2,v101))))) = Tern (v100,v102,(Tern (v100,v2,v101))) by A27; :: thesis: verum
end;
A87: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v3))))) = Tern (v0,v2,(Tern (v0,v3,v1)))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v3))))) = Tern (v0,v2,(Tern (v0,v3,v1)))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v3))))) = Tern (v0,v2,(Tern (v0,v3,v1))) by A84; :: thesis: verum
end;
A89: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v3))))) = Tern (v0,v2,(Tern (v0,v1,v3)))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v3))))) = Tern (v0,v2,(Tern (v0,v1,v3)))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v3))))) = Tern (v0,v2,(Tern (v0,v1,v3))) by A87; :: thesis: verum
end;
A92: for v100, v3, v102, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v102,v3)),v102) = Tern (v2,v102,(Tern (v102,v100,v3)))
proof
let v100, v3, v102, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v102,v3)),v102) = Tern (v2,v102,(Tern (v102,v100,v3)))
Tern (v102,v100,(Tern (v2,v102,v3))) = Tern (v2,v102,(Tern (v102,v100,v3))) by A45;
hence Tern (v100,(Tern (v2,v102,v3)),v102) = Tern (v2,v102,(Tern (v102,v100,v3))) by A3; :: thesis: verum
end;
A95: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v2,v0,v3)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v2,v0,v3)))
Tern (v0,(Tern (v1,v2,v3)),v2) = Tern (v0,v2,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v2,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v2,v0,v3))) by A92; :: thesis: verum
end;
A98: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v2,v1,(Tern (v0,v3,v1)))
proof
let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v2,v1,(Tern (v0,v3,v1)))
Tern (v0,v3,v1) = Tern (v1,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v2,v1,(Tern (v0,v3,v1))) by A95; :: thesis: verum
end;
A100: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v2,v1,(Tern (v0,v1,v3)))
proof
let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v2,v1,(Tern (v0,v1,v3)))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v2,v1,(Tern (v0,v1,v3))) by A98; :: thesis: verum
end;
A103: for v101, v1, v3, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v102,v1,v3)))))
proof
let v101, v1, v3, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v102,v1,v3)))))
Tern (v102,v1,(Tern (v100,v102,v3))) = Tern (v100,v102,(Tern (v102,v1,v3))) by A45;
hence Tern (v100,v101,(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v102,v1,v3))))) by A27; :: thesis: verum
end;
A107: for v100, v3, v1, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v1,v3)),(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v102,v1,v3)))
proof
let v100, v3, v1, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v1,v3)),(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v102,v1,v3)))
Tern (v102,v1,(Tern (v100,v102,v3))) = Tern (v100,v102,(Tern (v102,v1,v3))) by A45;
hence Tern (v100,(Tern (v102,v1,v3)),(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,v102,(Tern (v102,v1,v3))) by A63; :: thesis: verum
end;
A111: for v1, v3, v101, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v101,v1,(Tern (v100,v101,v3))))) = Tern (v100,v101,(Tern (v101,v1,v3)))
proof
let v1, v3, v101, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v101,v1,(Tern (v100,v101,v3))))) = Tern (v100,v101,(Tern (v101,v1,v3)))
Tern (v101,v1,(Tern (v100,v101,v3))) = Tern (v100,v101,(Tern (v101,v1,v3))) by A45;
hence Tern (v100,v101,(Tern (v101,v1,(Tern (v100,v101,v3))))) = Tern (v100,v101,(Tern (v101,v1,v3))) by A74; :: thesis: verum
end;
A115: for v101, v2, v3, v100, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v2,v102,(Tern (v102,v100,v3))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v2,v102,v3)))))
proof
let v101, v2, v3, v100, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v2,v102,(Tern (v102,v100,v3))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v2,v102,v3)))))
Tern (v102,v100,(Tern (v2,v102,v3))) = Tern (v2,v102,(Tern (v102,v100,v3))) by A45;
hence Tern (v100,v101,(Tern (v2,v102,(Tern (v102,v100,v3))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v2,v102,v3))))) by A45; :: thesis: verum
end;
A118: for v1, v2, v3, v4, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v4,v3))))) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v2, v3, v4, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v4,v3))))) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,v4,v3) = Tern (v3,v0,v4) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v4,v3))))) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A115; :: thesis: verum
end;
A120: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,v4,v3) = Tern (v0,v3,v4) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A118; :: thesis: verum
end;
A122: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3)
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3)
Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3) = Tern (v3,v0,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3) by A120; :: thesis: verum
end;
A124: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3) = Tern (v0,v3,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A122; :: thesis: verum
end;
A127: for v100, v3, v2, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v2,v3)),v102) = Tern (v102,v3,(Tern (v102,v100,v2)))
proof
let v100, v3, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v2,v3)),v102) = Tern (v102,v3,(Tern (v102,v100,v2)))
Tern (v102,v100,(Tern (v102,v2,v3))) = Tern (v102,v3,(Tern (v102,v100,v2))) by A55;
hence Tern (v100,(Tern (v102,v2,v3)),v102) = Tern (v102,v3,(Tern (v102,v100,v2))) by A3; :: thesis: verum
end;
A130: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v1,v0,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v1,v0,v2)))
Tern (v0,(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v1,v0,v2))) by A127; :: thesis: verum
end;
A132: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v0,v2,v1)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v0,v2,v1)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v0,v2,v1))) by A130; :: thesis: verum
end;
A134: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A132; :: thesis: verum
end;
A139: for v101, v102, v3, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v2,v3))))) = Tern (v100,v102,(Tern (v100,v3,(Tern (v100,v101,v2)))))
proof
let v101, v102, v3, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v2,v3))))) = Tern (v100,v102,(Tern (v100,v3,(Tern (v100,v101,v2)))))
Tern (v100,v101,(Tern (v100,v2,v3))) = Tern (v100,v3,(Tern (v100,v101,v2))) by A55;
hence Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v2,v3))))) = Tern (v100,v102,(Tern (v100,v3,(Tern (v100,v101,v2))))) by A27; :: thesis: verum
end;
A145: for v101, v1, v102, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v1,(Tern (v100,v2,v102))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v1,v2)))))
proof
let v101, v1, v102, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v1,(Tern (v100,v2,v102))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v1,v2)))))
Tern (v100,v1,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v1,v2))) by A55;
hence Tern (v100,v101,(Tern (v100,v1,(Tern (v100,v2,v102))))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v1,v2))))) by A27; :: thesis: verum
end;
A149: for v101, v1, v3, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,(Tern (v102,v1,v3)),(Tern (v100,v101,v102)))
proof
let v101, v1, v3, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,(Tern (v102,v1,v3)),(Tern (v100,v101,v102)))
Tern (v102,v1,(Tern (v100,v102,v3))) = Tern (v100,v102,(Tern (v102,v1,v3))) by A45;
hence Tern (v100,v101,(Tern (v102,v1,(Tern (v100,v102,v3))))) = Tern (v100,(Tern (v102,v1,v3)),(Tern (v100,v101,v102))) by A55; :: thesis: verum
end;
A155: for v100, v2, v4, v3, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v2,(Tern (v102,v3,v4)))),v102) = Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4)))))
proof
let v100, v2, v4, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v2,(Tern (v102,v3,v4)))),v102) = Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4)))))
Tern (v102,v100,(Tern (v102,v2,(Tern (v102,v3,v4))))) = Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4))))) by A59;
hence Tern (v100,(Tern (v102,v2,(Tern (v102,v3,v4)))),v102) = Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4))))) by A3; :: thesis: verum
end;
A158: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v1,v0,(Tern (v1,v2,v4)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v1,v0,(Tern (v1,v2,v4)))))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),v1) = Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v1,v0,(Tern (v1,v2,v4))))) by A155; :: thesis: verum
end;
A160: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v1)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v1)))
Tern (v0,(Tern (v1,v2,v4)),v1) = Tern (v1,v0,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v1))) by A158; :: thesis: verum
end;
A162: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v1,v2,v4)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v1,v2,v4)))))
Tern (v0,(Tern (v1,v2,v4)),v1) = Tern (v0,v1,(Tern (v1,v2,v4))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v1,v2,v4))))) by A160; :: thesis: verum
end;
A167: for v100, v1, v4, v2, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v1,(Tern (v102,v2,v4)))),v102) = Tern (v102,v1,(Tern (v102,v2,(Tern (v102,v100,v4)))))
proof
let v100, v1, v4, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v1,(Tern (v102,v2,v4)))),v102) = Tern (v102,v1,(Tern (v102,v2,(Tern (v102,v100,v4)))))
Tern (v102,v1,(Tern (v102,v2,(Tern (v102,v100,v4))))) = Tern (v102,v100,(Tern (v102,v1,(Tern (v102,v2,v4))))) by A59;
hence Tern (v100,(Tern (v102,v1,(Tern (v102,v2,v4)))),v102) = Tern (v102,v1,(Tern (v102,v2,(Tern (v102,v100,v4))))) by A3; :: thesis: verum
end;
A170: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v1,v0,v4)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v1,v0,v4)))))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),v1) = Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v1,v0,v4))))) by A167; :: thesis: verum
end;
A172: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,v1)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,v1)))))
Tern (v0,v4,v1) = Tern (v1,v0,v4) by A3;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,v1))))) by A170; :: thesis: verum
end;
A174: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v1,v4)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v1,v4)))))
Tern (v0,v4,v1) = Tern (v0,v1,v4) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v1,v4))))) by A172; :: thesis: verum
end;
A177: for v101, v3, v100, v4, v2, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4))))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v4)))))))
proof
let v101, v3, v100, v4, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4))))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v4)))))))
Tern (v102,v100,(Tern (v102,v2,(Tern (v102,v3,v4))))) = Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4))))) by A59;
hence Tern (v100,v101,(Tern (v102,v3,(Tern (v102,v100,(Tern (v102,v2,v4))))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v4))))))) by A45; :: thesis: verum
end;
A180: for v1, v3, v0, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,(Tern (v2,v4,v5)),v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))))
proof
let v1, v3, v0, v5, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,(Tern (v2,v4,v5)),v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))))
Tern (v0,(Tern (v2,v4,v5)),v2) = Tern (v2,v0,(Tern (v2,v4,v5))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,(Tern (v2,v4,v5)),v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5))))))) by A177; :: thesis: verum
end;
A182: for v1, v3, v0, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))))
proof
let v1, v3, v0, v5, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))))
Tern (v0,(Tern (v2,v4,v5)),v2) = Tern (v0,v2,(Tern (v2,v4,v5))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5))))))) by A180; :: thesis: verum
end;
A184: for v1, v3, v0, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))),v2)
proof
let v1, v3, v0, v5, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))),v2)
Tern (v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))),v2) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5))))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))),v2) by A182; :: thesis: verum
end;
A186: for v1, v3, v0, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))))
proof
let v1, v3, v0, v5, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))))
Tern (v0,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5)))))),v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5))))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,(Tern (v2,v4,v5))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v5))))))) by A184; :: thesis: verum
end;
A189: for v101, v102, v1, v3, v103, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v102,(Tern (v103,v1,(Tern (v100,v103,v3))))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v100,v102,(Tern (v103,v1,v3)))))))
proof
let v101, v102, v1, v3, v103, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v102,(Tern (v103,v1,(Tern (v100,v103,v3))))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v100,v102,(Tern (v103,v1,v3)))))))
Tern (v103,v1,(Tern (v100,v103,v3))) = Tern (v100,v103,(Tern (v103,v1,v3))) by A45;
hence Tern (v100,v101,(Tern (v100,v102,(Tern (v103,v1,(Tern (v100,v103,v3))))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v100,v102,(Tern (v103,v1,v3))))))) by A59; :: thesis: verum
end;
A193: for v3, v101, v4, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,v4))))) = Tern (v100,(Tern (v100,v3,v4)),(Tern (v100,v101,v102)))
proof
let v3, v101, v4, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,v4))))) = Tern (v100,(Tern (v100,v3,v4)),(Tern (v100,v101,v102)))
Tern (v100,v101,(Tern (v100,v102,(Tern (v100,v3,v4))))) = Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,v4))))) by A59;
hence Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,v4))))) = Tern (v100,(Tern (v100,v3,v4)),(Tern (v100,v101,v102))) by A55; :: thesis: verum
end;
A198: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern (v0,v4,(Tern (v0,v1,v2)))))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern (v0,v4,(Tern (v0,v1,v2)))))
Tern (v0,v1,(Tern (v0,v2,v4))) = Tern (v0,v4,(Tern (v0,v1,v2))) by A55;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) by A59; :: thesis: verum
end;
A201: for v100, v2, v3, v101, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v101,v3))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v2,v3)))))
proof
let v100, v2, v3, v101, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v101,v3))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v2,v3)))))
Tern (v102,v101,(Tern (v102,v2,v3))) = Tern (v102,v2,(Tern (v102,v101,v3))) by A27;
hence Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v101,v3))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v2,v3))))) by A100; :: thesis: verum
end;
A204: for v0, v3, v2, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v3, v2, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,v4,v2) = Tern (v2,v1,v4) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A201; :: thesis: verum
end;
A206: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,v4,v2) = Tern (v1,v2,v4) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A204; :: thesis: verum
end;
A208: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v2)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v2)
Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v2) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v2) by A206; :: thesis: verum
end;
A210: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A208; :: thesis: verum
end;
A213: for v100, v101, v2, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v2,v101))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v2,v101)))))
proof
let v100, v101, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v2,v101))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v2,v101)))))
Tern (v102,v101,(Tern (v102,v2,v101))) = Tern (v102,v2,v101) by A63;
hence Tern (v100,v101,(Tern (v102,v2,v101))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v2,v101))))) by A100; :: thesis: verum
end;
A216: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v1)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v1)))))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v3,v1))))) by A213; :: thesis: verum
end;
A218: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v1,v2,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v1,v2,v3)))))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A216; :: thesis: verum
end;
A220: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2)
Tern (v1,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2) = Tern (v2,v1,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A3;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2) by A218; :: thesis: verum
end;
A222: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))
Tern (v1,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A220; :: thesis: verum
end;
A227: for v100, v2, v3, v101, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v2,v102,(Tern (v102,v101,v3))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v2,v102,v3)))))
proof
let v100, v2, v3, v101, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v2,v102,(Tern (v102,v101,v3))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v2,v102,v3)))))
Tern (v102,v101,(Tern (v2,v102,v3))) = Tern (v2,v102,(Tern (v102,v101,v3))) by A45;
hence Tern (v100,v101,(Tern (v2,v102,(Tern (v102,v101,v3))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v2,v102,v3))))) by A100; :: thesis: verum
end;
A230: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v3))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v3))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,v4,v3) = Tern (v3,v1,v4) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v3))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A227; :: thesis: verum
end;
A232: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,v4,v3) = Tern (v1,v3,v4) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A230; :: thesis: verum
end;
A234: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3)
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3)
Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3) by A232; :: thesis: verum
end;
A236: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,(Tern (v0,v1,(Tern (v2,v3,v4)))),v3) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v3,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A234; :: thesis: verum
end;
A239: for v101, v2, v3, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v2,v102,(Tern (v100,v102,v3))))) = Tern (v100,(Tern (v2,v102,v3)),(Tern (v100,v101,v102)))
proof
let v101, v2, v3, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v2,v102,(Tern (v100,v102,v3))))) = Tern (v100,(Tern (v2,v102,v3)),(Tern (v100,v101,v102)))
Tern (v100,v102,(Tern (v2,v102,v3))) = Tern (v2,v102,(Tern (v100,v102,v3))) by A100;
hence Tern (v100,v101,(Tern (v2,v102,(Tern (v100,v102,v3))))) = Tern (v100,(Tern (v2,v102,v3)),(Tern (v100,v101,v102))) by A55; :: thesis: verum
end;
A245: for v101, v2, v100, v3, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v100))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v100)))))))
proof
let v101, v2, v100, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v100))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v100)))))))
Tern (v102,v100,(Tern (v102,v2,(Tern (v102,v3,v100))))) = Tern (v102,v2,(Tern (v102,v3,v100))) by A78;
hence Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v100))))) = Tern (v102,v100,(Tern (v100,v101,(Tern (v102,v2,(Tern (v102,v3,v100))))))) by A45; :: thesis: verum
end;
A248: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,v0)))))))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,v0)))))))
Tern (v2,v4,v0) = Tern (v0,v2,v4) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,v0))))))) by A245; :: thesis: verum
end;
A250: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
Tern (v2,v4,v0) = Tern (v0,v2,v4) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))))) by A248; :: thesis: verum
end;
A252: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))),v2)
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))),v2)
Tern (v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))),v2) = Tern (v2,v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))),v2) by A250; :: thesis: verum
end;
A254: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
Tern (v0,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))),v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))))) by A252; :: thesis: verum
end;
A259: for v102, v2, v101, v3, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v3,v101))))))) = Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v3,v101)))))
proof
let v102, v2, v101, v3, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v3,v101))))))) = Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v3,v101)))))
Tern (v100,v101,(Tern (v100,v2,(Tern (v100,v3,v101))))) = Tern (v100,v2,(Tern (v100,v3,v101))) by A78;
hence Tern (v100,v101,(Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v3,v101))))))) = Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v3,v101))))) by A100; :: thesis: verum
end;
A262: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v4,v1)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v4,v1)))))
Tern (v0,v4,v1) = Tern (v0,v1,v4) by A4;
hence Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v4,v1))))) by A259; :: thesis: verum
end;
A264: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v4,v1)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v4,v1)))))
Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A3;
hence Tern (v0,v1,(Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v4,v1))))) by A262; :: thesis: verum
end;
A267: for v4, v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))))) = Tern (v4,v1,(Tern (v0,v2,(Tern (v0,v3,v1)))))
proof
let v4, v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))))) = Tern (v4,v1,(Tern (v0,v2,(Tern (v0,v3,v1)))))
Tern (v1,(Tern (v0,v2,(Tern (v0,v1,v3)))),v4) = Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))) by A4;
hence Tern (v0,v1,(Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))))) = Tern (v4,v1,(Tern (v0,v2,(Tern (v0,v3,v1))))) by A264; :: thesis: verum
end;
A270: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4)))))
Tern (v0,v4,v1) = Tern (v0,v1,v4) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A267; :: thesis: verum
end;
A272: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2)
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2)
Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A3;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2) by A270; :: thesis: verum
end;
A274: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4)))))
Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2) = Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A272; :: thesis: verum
end;
A277: for v102, v100, v3, v103, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v103,v3)),(Tern (v100,v102,(Tern (v100,v103,(Tern (v2,v103,v3))))))) = Tern (v100,v102,(Tern (v2,v103,(Tern (v100,v103,v3)))))
proof
let v102, v100, v3, v103, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v103,v3)),(Tern (v100,v102,(Tern (v100,v103,(Tern (v2,v103,v3))))))) = Tern (v100,v102,(Tern (v2,v103,(Tern (v100,v103,v3)))))
Tern (v100,v103,(Tern (v2,v103,v3))) = Tern (v2,v103,(Tern (v100,v103,v3))) by A100;
hence Tern (v100,(Tern (v2,v103,v3)),(Tern (v100,v102,(Tern (v100,v103,(Tern (v2,v103,v3))))))) = Tern (v100,v102,(Tern (v2,v103,(Tern (v100,v103,v3))))) by A78; :: thesis: verum
end;
A280: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v4,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v4,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern (v0,v4,(Tern (v0,v2,(Tern (v1,v2,v3))))) by A78;
hence Tern (v0,v4,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A277; :: thesis: verum
end;
A286: for v100, v101, v3, v1, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v101,v102,(Tern (v100,v101,(Tern (v102,v1,v3))))))) = Tern (v100,v101,(Tern (v102,v1,(Tern (v101,v102,v3)))))
proof
let v100, v101, v3, v1, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v101,v102,(Tern (v100,v101,(Tern (v102,v1,v3))))))) = Tern (v100,v101,(Tern (v102,v1,(Tern (v101,v102,v3)))))
Tern (v102,v1,(Tern (v101,v102,v3))) = Tern (v101,v102,(Tern (v102,v1,v3))) by A45;
hence Tern (v100,v101,(Tern (v101,v102,(Tern (v100,v101,(Tern (v102,v1,v3))))))) = Tern (v100,v101,(Tern (v102,v1,(Tern (v101,v102,v3))))) by A111; :: thesis: verum
end;
A289: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4)))))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4)))))
Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,v4))))))) = Tern (v0,v1,(Tern (v1,v2,(Tern (v2,v3,v4))))) by A111;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) by A286; :: thesis: verum
end;
A293: for v102, v100, v3, v2, v101 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v101,v102,(Tern (v100,v101,(Tern (v101,v2,v3))))))) = Tern (v100,v101,(Tern (v101,v3,(Tern (v101,v102,v2)))))
proof
let v102, v100, v3, v2, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v101,v102,(Tern (v100,v101,(Tern (v101,v2,v3))))))) = Tern (v100,v101,(Tern (v101,v3,(Tern (v101,v102,v2)))))
Tern (v101,v102,(Tern (v101,v2,v3))) = Tern (v101,v3,(Tern (v101,v102,v2))) by A55;
hence Tern (v100,v101,(Tern (v101,v102,(Tern (v100,v101,(Tern (v101,v2,v3))))))) = Tern (v100,v101,(Tern (v101,v3,(Tern (v101,v102,v2))))) by A111; :: thesis: verum
end;
A296: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3)))))
Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v1,(Tern (v1,v3,v4))))))) = Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) by A111;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))) by A293; :: thesis: verum
end;
A299: for v2, v3, v100, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v102,(Tern (v102,v100,v3)))),v102) = Tern (v2,v102,(Tern (v102,v100,v3)))
proof
let v2, v3, v100, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v102,(Tern (v102,v100,v3)))),v102) = Tern (v2,v102,(Tern (v102,v100,v3)))
Tern (v102,v100,(Tern (v2,v102,(Tern (v102,v100,v3))))) = Tern (v2,v102,(Tern (v102,v100,v3))) by A222;
hence Tern (v100,(Tern (v2,v102,(Tern (v102,v100,v3)))),v102) = Tern (v2,v102,(Tern (v102,v100,v3))) by A3; :: thesis: verum
end;
A302: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v2)))),v2) = Tern (v1,v2,(Tern (v2,v0,v3)))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v2)))),v2) = Tern (v1,v2,(Tern (v2,v0,v3)))
Tern (v0,v3,v2) = Tern (v2,v0,v3) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v2)))),v2) = Tern (v1,v2,(Tern (v2,v0,v3))) by A299; :: thesis: verum
end;
A304: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v2) = Tern (v1,v2,(Tern (v2,v0,v3)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v2) = Tern (v1,v2,(Tern (v2,v0,v3)))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v2) = Tern (v1,v2,(Tern (v2,v0,v3))) by A302; :: thesis: verum
end;
A306: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v1,v2,(Tern (v2,v0,v3)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v1,v2,(Tern (v2,v0,v3)))
Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v2) = Tern (v0,v2,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A4;
hence Tern (v0,v2,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v1,v2,(Tern (v2,v0,v3))) by A304; :: thesis: verum
end;
A309: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v1,v3))))) = Tern (v2,v1,(Tern (v0,v3,v1)))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v1,v3))))) = Tern (v2,v1,(Tern (v0,v3,v1)))
Tern (v0,v3,v1) = Tern (v1,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v1,v3))))) = Tern (v2,v1,(Tern (v0,v3,v1))) by A306; :: thesis: verum
end;
A311: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v1,v3))))) = Tern (v2,v1,(Tern (v0,v1,v3)))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v1,v3))))) = Tern (v2,v1,(Tern (v0,v1,v3)))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v1,v3))))) = Tern (v2,v1,(Tern (v0,v1,v3))) by A309; :: thesis: verum
end;
A314: for v102, v2, v3, v101, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v101,v3))))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v100,v2,v3)))))
proof
let v102, v2, v3, v101, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v101,v3))))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v100,v2,v3)))))
Tern (v100,v101,(Tern (v100,v2,v3))) = Tern (v100,v2,(Tern (v100,v101,v3))) by A27;
hence Tern (v100,v101,(Tern (v102,v101,(Tern (v100,v2,(Tern (v100,v101,v3))))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v100,v2,v3))))) by A311; :: thesis: verum
end;
A317: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v4)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v4)))))
Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2) = Tern (v2,v1,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A3;
hence Tern (v0,v1,(Tern (v1,(Tern (v0,v3,(Tern (v0,v1,v4)))),v2))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v4))))) by A314; :: thesis: verum
end;
A320: for v4, v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))))) = Tern (v4,v1,(Tern (v0,v1,(Tern (v0,v2,v3)))))
proof
let v4, v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))))) = Tern (v4,v1,(Tern (v0,v1,(Tern (v0,v2,v3)))))
Tern (v1,(Tern (v0,v2,(Tern (v0,v1,v3)))),v4) = Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))) by A4;
hence Tern (v0,v1,(Tern (v1,v4,(Tern (v0,v2,(Tern (v0,v1,v3))))))) = Tern (v4,v1,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A317; :: thesis: verum
end;
A323: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v4)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v4)))))
Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))) by A274;
hence Tern (v1,v2,(Tern (v0,v3,(Tern (v0,v1,v4))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v4))))) by A320; :: thesis: verum
end;
A326: for v1, v3, v4, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v0,v4))))) = Tern (v0,(Tern (v2,v0,(Tern (v2,v3,v4)))),v1)
proof
let v1, v3, v4, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v0,v4))))) = Tern (v0,(Tern (v2,v0,(Tern (v2,v3,v4)))),v1)
Tern (v0,(Tern (v2,v0,(Tern (v2,v3,v4)))),v1) = Tern (v1,v0,(Tern (v2,v0,(Tern (v2,v3,v4))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v0,v4))))) = Tern (v0,(Tern (v2,v0,(Tern (v2,v3,v4)))),v1) by A323; :: thesis: verum
end;
A328: for v1, v3, v4, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v0,v4))))) = Tern (v0,v1,(Tern (v2,v0,(Tern (v2,v3,v4)))))
proof
let v1, v3, v4, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v0,v4))))) = Tern (v0,v1,(Tern (v2,v0,(Tern (v2,v3,v4)))))
Tern (v0,(Tern (v2,v0,(Tern (v2,v3,v4)))),v1) = Tern (v0,v1,(Tern (v2,v0,(Tern (v2,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v0,v4))))) = Tern (v0,v1,(Tern (v2,v0,(Tern (v2,v3,v4))))) by A326; :: thesis: verum
end;
A331: for v101, v104, v102, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v102,v104))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v102,(Tern (v100,v102,v104)),v104)))))
proof
let v101, v104, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v102,v104))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v102,(Tern (v100,v102,v104)),v104)))))
Tern (v102,(Tern (v100,v102,v104)),(Tern (v100,v102,v104))) = Tern (v100,v102,v104) by A34;
hence Tern (v100,v101,(Tern (v100,v102,v104))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v102,(Tern (v100,v102,v104)),v104))))) by A103; :: thesis: verum
end;
A334: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3)))))))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3)))))))
Tern (v2,(Tern (v0,v2,v3)),v3) = Tern (v2,v3,(Tern (v0,v2,v3))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3))))))) by A331; :: thesis: verum
end;
A336: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3)))))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3)))))
Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3))))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3))))) by A254;
hence Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v3))))) by A334; :: thesis: verum
end;
A340: for v2, v3, v1, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v102,v1,v3)))),v102) = Tern (v102,v1,(Tern (v1,v2,v3)))
proof
let v2, v3, v1, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v102,v1,v3)))),v102) = Tern (v102,v1,(Tern (v1,v2,v3)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v102,v1,v3))))) = Tern (v102,v1,(Tern (v1,v2,v3))) by A107;
hence Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v102,v1,v3)))),v102) = Tern (v102,v1,(Tern (v1,v2,v3))) by A3; :: thesis: verum
end;
A343: for v1, v0, v3, v2 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v2,v3,v0)))),v3) = Tern (v3,v0,(Tern (v0,v1,v2)))
proof
let v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v2,v3,v0)))),v3) = Tern (v3,v0,(Tern (v0,v1,v2)))
Tern (v3,v0,v2) = Tern (v2,v3,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v2,v3,v0)))),v3) = Tern (v3,v0,(Tern (v0,v1,v2))) by A340; :: thesis: verum
end;
A345: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3)))),v3) = Tern (v3,v0,(Tern (v0,v1,v2)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3)))),v3) = Tern (v3,v0,(Tern (v0,v1,v2)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3)))),v3) = Tern (v3,v0,(Tern (v0,v1,v2))) by A343; :: thesis: verum
end;
A347: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3))))) = Tern (v3,v0,(Tern (v0,v1,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3))))) = Tern (v3,v0,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3)))),v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3))))) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3))))) = Tern (v3,v0,(Tern (v0,v1,v2))) by A345; :: thesis: verum
end;
A350: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v3,v0))))) = Tern (v1,(Tern (v1,v2,v3)),v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v3,v0))))) = Tern (v1,(Tern (v1,v2,v3)),v0)
Tern (v1,(Tern (v1,v2,v3)),v0) = Tern (v0,v1,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v3,v0))))) = Tern (v1,(Tern (v1,v2,v3)),v0) by A347; :: thesis: verum
end;
A352: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v3,v0))))) = Tern (v1,v0,(Tern (v1,v2,v3)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v3,v0))))) = Tern (v1,v0,(Tern (v1,v2,v3)))
Tern (v1,(Tern (v1,v2,v3)),v0) = Tern (v1,v0,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v3,v0))))) = Tern (v1,v0,(Tern (v1,v2,v3))) by A350; :: thesis: verum
end;
A355: for v101, v102, v3, v4, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,(Tern (v2,v3,(Tern (v100,v2,v4)))))),(Tern (v101,v102,(Tern (v100,v2,(Tern (v100,v101,(Tern (v2,v3,v4))))))))) = Tern (v100,v101,(Tern (v101,v102,(Tern (v2,v3,(Tern (v100,v2,v4)))))))
proof
let v101, v102, v3, v4, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,(Tern (v2,v3,(Tern (v100,v2,v4)))))),(Tern (v101,v102,(Tern (v100,v2,(Tern (v100,v101,(Tern (v2,v3,v4))))))))) = Tern (v100,v101,(Tern (v101,v102,(Tern (v2,v3,(Tern (v100,v2,v4)))))))
Tern (v100,v101,(Tern (v2,v3,(Tern (v100,v2,v4))))) = Tern (v100,v2,(Tern (v100,v101,(Tern (v2,v3,v4))))) by A103;
hence Tern (v100,(Tern (v101,v102,(Tern (v2,v3,(Tern (v100,v2,v4)))))),(Tern (v101,v102,(Tern (v100,v2,(Tern (v100,v101,(Tern (v2,v3,v4))))))))) = Tern (v100,v101,(Tern (v101,v102,(Tern (v2,v3,(Tern (v100,v2,v4))))))) by A107; :: thesis: verum
end;
A359: for v3, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,(Tern (v100,v2,v3)))),(Tern (v100,v2,v3))) = Tern (v2,v3,(Tern (v100,v2,v3)))
proof
let v3, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,(Tern (v100,v2,v3)))),(Tern (v100,v2,v3))) = Tern (v2,v3,(Tern (v100,v2,v3)))
Tern (v100,(Tern (v2,v3,(Tern (v100,v2,v3)))),(Tern (v2,v3,(Tern (v100,v2,v3))))) = Tern (v100,(Tern (v2,v3,(Tern (v100,v2,v3)))),(Tern (v100,v2,v3))) by A336;
hence Tern (v100,(Tern (v2,v3,(Tern (v100,v2,v3)))),(Tern (v100,v2,v3))) = Tern (v2,v3,(Tern (v100,v2,v3))) by A34; :: thesis: verum
end;
A362: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v2))))) = Tern (v1,v2,(Tern (v0,v1,v2)))
proof
let v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v2))))) = Tern (v1,v2,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v2))))) by A4;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v2))))) = Tern (v1,v2,(Tern (v0,v1,v2))) by A359; :: thesis: verum
end;
A364: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v0,v1,v2)))
proof
let v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) by A336;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v0,v1,v2))) by A362; :: thesis: verum
end;
A366: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,v2)))
proof
let v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A34;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,v2))) by A364; :: thesis: verum
end;
A371: for v100, v2, v4, v3, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,(Tern (v102,v3,v4)))),v102) = Tern (v102,v3,(Tern (v102,v100,(Tern (v2,v3,v4)))))
proof
let v100, v2, v4, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,(Tern (v102,v3,v4)))),v102) = Tern (v102,v3,(Tern (v102,v100,(Tern (v2,v3,v4)))))
Tern (v102,v100,(Tern (v2,v3,(Tern (v102,v3,v4))))) = Tern (v102,v3,(Tern (v102,v100,(Tern (v2,v3,v4))))) by A124;
hence Tern (v100,(Tern (v2,v3,(Tern (v102,v3,v4)))),v102) = Tern (v102,v3,(Tern (v102,v100,(Tern (v2,v3,v4))))) by A3; :: thesis: verum
end;
A374: for v0, v1, v3, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v4,v3)))),v3) = Tern (v3,v2,(Tern (v3,v0,(Tern (v1,v2,v4)))))
proof
let v0, v1, v3, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v4,v3)))),v3) = Tern (v3,v2,(Tern (v3,v0,(Tern (v1,v2,v4)))))
Tern (v2,v4,v3) = Tern (v3,v2,v4) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v4,v3)))),v3) = Tern (v3,v2,(Tern (v3,v0,(Tern (v1,v2,v4))))) by A371; :: thesis: verum
end;
A377: for v0, v1, v3, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v4,v3)))),v4) = Tern (v4,v2,(Tern (v4,v0,(Tern (v1,v2,v3)))))
proof
let v0, v1, v3, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v4,v3)))),v4) = Tern (v4,v2,(Tern (v4,v0,(Tern (v1,v2,v3)))))
Tern (v2,v3,v4) = Tern (v2,v4,v3) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v4,v3)))),v4) = Tern (v4,v2,(Tern (v4,v0,(Tern (v1,v2,v3))))) by A374; :: thesis: verum
end;
A380: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v1,v2,(Tern (v2,v3,v4))))) = Tern (v3,v2,(Tern (v3,v0,(Tern (v1,v2,v4)))))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v1,v2,(Tern (v2,v3,v4))))) = Tern (v3,v2,(Tern (v3,v0,(Tern (v1,v2,v4)))))
Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),v3) = Tern (v0,v3,(Tern (v1,v2,(Tern (v2,v3,v4))))) by A4;
hence Tern (v0,v3,(Tern (v1,v2,(Tern (v2,v3,v4))))) = Tern (v3,v2,(Tern (v3,v0,(Tern (v1,v2,v4))))) by A377; :: thesis: verum
end;
A383: for v0, v2, v4, v1, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v1,v3,(Tern (v0,(Tern (v2,v3,v4)),v1)))
proof
let v0, v2, v4, v1, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v1,v3,(Tern (v0,(Tern (v2,v3,v4)),v1)))
Tern (v0,(Tern (v2,v3,v4)),v1) = Tern (v1,v0,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v1,v3,(Tern (v0,(Tern (v2,v3,v4)),v1))) by A380; :: thesis: verum
end;
A385: for v0, v2, v4, v1, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v2, v4, v1, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,(Tern (v2,v3,v4)),v1) = Tern (v0,v1,(Tern (v2,v3,v4))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A383; :: thesis: verum
end;
A387: for v0, v2, v4, v1, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v3,(Tern (v0,v1,(Tern (v2,v3,v4)))),v1)
proof
let v0, v2, v4, v1, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v3,(Tern (v0,v1,(Tern (v2,v3,v4)))),v1)
Tern (v3,(Tern (v0,v1,(Tern (v2,v3,v4)))),v1) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v3,(Tern (v0,v1,(Tern (v2,v3,v4)))),v1) by A385; :: thesis: verum
end;
A389: for v0, v2, v4, v1, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v2, v4, v1, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v3,(Tern (v0,v1,(Tern (v2,v3,v4)))),v1) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v1,v4))))) = Tern (v3,v1,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A387; :: thesis: verum
end;
A392: for v102, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v102,v4,v1)),v102) = Tern (v102,v4,(Tern (v1,v2,(Tern (v102,v1,v3)))))
proof
let v102, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v102,v4,v1)),v102) = Tern (v102,v4,(Tern (v1,v2,(Tern (v102,v1,v3)))))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v4,v1))) = Tern (v102,v4,(Tern (v1,v2,(Tern (v102,v1,v3))))) by A149;
hence Tern ((Tern (v1,v2,v3)),(Tern (v102,v4,v1)),v102) = Tern (v102,v4,(Tern (v1,v2,(Tern (v102,v1,v3))))) by A3; :: thesis: verum
end;
A395: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,v4,(Tern (v0,v1,(Tern (v3,v0,v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,v4,(Tern (v0,v1,(Tern (v3,v0,v2)))))
Tern (v3,v4,v0) = Tern (v0,v3,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,v4,(Tern (v0,v1,(Tern (v3,v0,v2))))) by A392; :: thesis: verum
end;
A397: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v3,v0,v2)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v3,v0,v2)))))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v3,v0,v2))))) by A395; :: thesis: verum
end;
A400: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v3,v0,v1)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v3,v0,v1)))))
Tern (v0,v1,v3) = Tern (v3,v0,v1) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v3,v0,v1))))) by A397; :: thesis: verum
end;
A402: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v0)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v0)))))
Tern (v3,v0,v1) = Tern (v1,v3,v0) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v0))))) by A400; :: thesis: verum
end;
A405: for v100, v2, v3, v1, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v2,(Tern (v102,v1,v3)))),v102) = Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v100,v1)))
proof
let v100, v2, v3, v1, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v2,(Tern (v102,v1,v3)))),v102) = Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v100,v1)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v100,v1))) = Tern (v102,v100,(Tern (v1,v2,(Tern (v102,v1,v3))))) by A149;
hence Tern (v100,(Tern (v1,v2,(Tern (v102,v1,v3)))),v102) = Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v100,v1))) by A3; :: thesis: verum
end;
A408: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v1,v4,v3)))),v3) = Tern (v3,(Tern (v1,v2,v4)),(Tern (v3,v0,v1)))
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v1,v4,v3)))),v3) = Tern (v3,(Tern (v1,v2,v4)),(Tern (v3,v0,v1)))
Tern (v1,v4,v3) = Tern (v3,v1,v4) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v1,v4,v3)))),v3) = Tern (v3,(Tern (v1,v2,v4)),(Tern (v3,v0,v1))) by A405; :: thesis: verum
end;
A411: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v1,v4,v3)))),v4) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v4,v0,v1)))
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v1,v4,v3)))),v4) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v4,v0,v1)))
Tern (v1,v3,v4) = Tern (v1,v4,v3) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v1,v4,v3)))),v4) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v4,v0,v1))) by A408; :: thesis: verum
end;
A414: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v3,(Tern (v1,v2,v4)),(Tern (v3,v0,v1)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v3,(Tern (v1,v2,v4)),(Tern (v3,v0,v1)))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),v3) = Tern (v0,v3,(Tern (v1,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern (v0,v3,(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern (v3,(Tern (v1,v2,v4)),(Tern (v3,v0,v1))) by A411; :: thesis: verum
end;
A417: for v0, v3, v4, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v2,v1,v0)))
proof
let v0, v3, v4, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v2,v1,v0)))
Tern (v1,v0,v2) = Tern (v2,v1,v0) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v2,v1,v0))) by A414; :: thesis: verum
end;
A419: for v0, v3, v4, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v1)))
proof
let v0, v3, v4, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v1)))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v1))) by A417; :: thesis: verum
end;
A423: for v4, v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v3,v1)),(Tern (v0,v4,v1))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v4, v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v2,v3,v1)),(Tern (v0,v4,v1))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern (v0,(Tern (v2,v3,v1)),(Tern (v0,v4,v1))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A149; :: thesis: verum
end;
A426: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v3,v1,(Tern (v0,v3,v2)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v3,v1,(Tern (v0,v3,v2)))))
Tern (v0,v4,v3) = Tern (v0,v3,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v3,v1,(Tern (v0,v3,v2))))) by A423; :: thesis: verum
end;
A428: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v3,v1,(Tern (v0,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v3,v1,(Tern (v0,v2,v3)))))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v3,v1,(Tern (v0,v2,v3))))) by A426; :: thesis: verum
end;
A430: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v1,(Tern (v0,v2,v3)),v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v1,(Tern (v0,v2,v3)),v3)))
Tern (v1,(Tern (v0,v2,v3)),v3) = Tern (v3,v1,(Tern (v0,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v1,(Tern (v0,v2,v3)),v3))) by A428; :: thesis: verum
end;
A432: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v1,v3,(Tern (v0,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v1,v3,(Tern (v0,v2,v3)))))
Tern (v1,(Tern (v0,v2,v3)),v3) = Tern (v1,v3,(Tern (v0,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v1,v3,(Tern (v0,v2,v3))))) by A430; :: thesis: verum
end;
A435: for v103, v102, v2, v104, v100 being Element of (BA2TBAA B) holds Tern (v100,(Tern ((Tern (v100,v104,v2)),v102,v103)),(Tern (v100,v104,v2))) = Tern (v100,v104,(Tern ((Tern (v100,v104,v2)),v102,(Tern (v100,(Tern (v100,v104,v2)),v103)))))
proof
let v103, v102, v2, v104, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern ((Tern (v100,v104,v2)),v102,v103)),(Tern (v100,v104,v2))) = Tern (v100,v104,(Tern ((Tern (v100,v104,v2)),v102,(Tern (v100,(Tern (v100,v104,v2)),v103)))))
Tern (v100,v104,(Tern (v100,v104,v2))) = Tern (v100,v104,v2) by A74;
hence Tern (v100,(Tern ((Tern (v100,v104,v2)),v102,v103)),(Tern (v100,v104,v2))) = Tern (v100,v104,(Tern ((Tern (v100,v104,v2)),v102,(Tern (v100,(Tern (v100,v104,v2)),v103))))) by A149; :: thesis: verum
end;
A438: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),v4)))))
Tern ((Tern (v0,v1,v2)),v3,v4) = Tern (v4,(Tern (v0,v1,v2)),v3) by A3;
hence Tern (v0,(Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),v4))))) by A435; :: thesis: verum
end;
A441: for v4, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v4,v1,(Tern (v0,v2,v3)))),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern ((Tern (v0,v2,v3)),v4,(Tern (v0,(Tern (v0,v2,v3)),v1)))))
proof
let v4, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v4,v1,(Tern (v0,v2,v3)))),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern ((Tern (v0,v2,v3)),v4,(Tern (v0,(Tern (v0,v2,v3)),v1)))))
Tern (v1,(Tern (v0,v2,v3)),v4) = Tern (v4,v1,(Tern (v0,v2,v3))) by A3;
hence Tern (v0,(Tern (v4,v1,(Tern (v0,v2,v3)))),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern ((Tern (v0,v2,v3)),v4,(Tern (v0,(Tern (v0,v2,v3)),v1))))) by A438; :: thesis: verum
end;
A444: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern ((Tern (v0,v3,v4)),v1,(Tern (v0,(Tern (v0,v3,v4)),v2)))))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern ((Tern (v0,v3,v4)),v1,(Tern (v0,(Tern (v0,v3,v4)),v2)))))
Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v4)))),(Tern (v0,v3,v4))) = Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4))))) by A4;
hence Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4))))) = Tern (v0,v3,(Tern ((Tern (v0,v3,v4)),v1,(Tern (v0,(Tern (v0,v3,v4)),v2))))) by A441; :: thesis: verum
end;
A447: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2)))))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2)))))))
Tern (v0,(Tern (v0,v1,v2)),v4) = Tern (v0,v4,(Tern (v0,v1,v2))) by A4;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))))) by A444; :: thesis: verum
end;
A449: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))))
Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))))) by A447; :: thesis: verum
end;
A451: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))))))
Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))) by A4;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))))) by A449; :: thesis: verum
end;
A456: for v101, v3, v100, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v101,(Tern (v102,v100,v3))))) = Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100)))
proof
let v101, v3, v100, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v101,(Tern (v102,v100,v3))))) = Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100)))
Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v100,v3))))) by A149;
hence Tern (v100,v101,(Tern (v102,v101,(Tern (v102,v100,v3))))) = Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100))) by A100; :: thesis: verum
end;
A459: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v3,v2))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v3,v2))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
Tern (v0,v3,v2) = Tern (v2,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v3,v2))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0))) by A456; :: thesis: verum
end;
A461: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,v1,(Tern (v2,v1,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0))) by A459; :: thesis: verum
end;
A463: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,(Tern (v0,v2,v3)),v2))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,(Tern (v0,v2,v3)),v2))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
Tern (v1,(Tern (v0,v2,v3)),v2) = Tern (v2,v1,(Tern (v0,v2,v3))) by A3;
hence Tern (v0,v1,(Tern (v1,(Tern (v0,v2,v3)),v2))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0))) by A461; :: thesis: verum
end;
A465: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0)))
Tern (v1,(Tern (v0,v2,v3)),v2) = Tern (v1,v2,(Tern (v0,v2,v3))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v2,v1,v0))) by A463; :: thesis: verum
end;
A467: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v2,v1)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v2,v1)))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v2,v1))) by A465; :: thesis: verum
end;
A469: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A467; :: thesis: verum
end;
A474: for v102, v3, v101, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v100,v3)))))
proof
let v102, v3, v101, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v100,v3)))))
Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v100,v3))))) by A149;
hence Tern (v100,v101,(Tern (v102,(Tern (v100,v101,v3)),(Tern (v102,v101,v100))))) = Tern (v102,v101,(Tern (v100,v101,(Tern (v102,v100,v3))))) by A311; :: thesis: verum
end;
A477: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v2,v1))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v0,v3)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v2,v1))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v0,v3)))))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v2,v1))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v0,v3))))) by A474; :: thesis: verum
end;
A479: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v0,v3)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v0,v3)))))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v2,v0,v3))))) by A477; :: thesis: verum
end;
A481: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v2)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v2)))))
Tern (v0,v3,v2) = Tern (v2,v0,v3) by A3;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v3,v2))))) by A479; :: thesis: verum
end;
A483: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v2,v3)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v2,v3)))))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A481; :: thesis: verum
end;
A485: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v1,(Tern (v0,v1,(Tern (v0,v2,v3)))),v2)
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v1,(Tern (v0,v1,(Tern (v0,v2,v3)))),v2)
Tern (v1,(Tern (v0,v1,(Tern (v0,v2,v3)))),v2) = Tern (v2,v1,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A3;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v1,(Tern (v0,v1,(Tern (v0,v2,v3)))),v2) by A483; :: thesis: verum
end;
A487: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3)))))
Tern (v1,(Tern (v0,v1,(Tern (v0,v2,v3)))),v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A4;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A485; :: thesis: verum
end;
A489: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) by A149;
hence Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v2,v3,v4))))) by A103; :: thesis: verum
end;
A492: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,v3)))))
Tern (v0,v4,v1) = Tern (v0,v1,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,v3))))) by A489; :: thesis: verum
end;
A495: for v100, v104, v103, v101 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v101,v103,v104))) = Tern (v101,v104,(Tern (v101,v103,(Tern (v100,v101,v104)))))
proof
let v100, v104, v103, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v101,v103,v104))) = Tern (v101,v104,(Tern (v101,v103,(Tern (v100,v101,v104)))))
Tern (v101,v104,(Tern (v101,v103,v104))) = Tern (v101,v103,v104) by A63;
hence Tern (v100,v101,(Tern (v101,v103,v104))) = Tern (v101,v104,(Tern (v101,v103,(Tern (v100,v101,v104))))) by A174; :: thesis: verum
end;
A501: for v3, v101, v102, v100 being Element of (BA2TBAA B) holds Tern (v3,v100,(Tern (v100,v102,v101))) = Tern (v100,(Tern (v3,v100,v101)),(Tern (v100,v101,v102)))
proof
let v3, v101, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v3,v100,(Tern (v100,v102,v101))) = Tern (v100,(Tern (v3,v100,v101)),(Tern (v100,v101,v102)))
Tern (v100,v101,(Tern (v100,v102,(Tern (v3,v100,v101))))) = Tern (v3,v100,(Tern (v100,v102,v101))) by A495;
hence Tern (v3,v100,(Tern (v100,v102,v101))) = Tern (v100,(Tern (v3,v100,v101)),(Tern (v100,v101,v102))) by A55; :: thesis: verum
end;
A504: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v2,v3)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v2,v3)))
Tern (v1,v3,v2) = Tern (v1,v2,v3) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v2,v3))) by A501; :: thesis: verum
end;
A509: for v3, v2, v102, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v102,v2)),(Tern (v102,v3,v2)),v102) = Tern (v1,v102,(Tern (v102,v3,v2)))
proof
let v3, v2, v102, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v102,v2)),(Tern (v102,v3,v2)),v102) = Tern (v1,v102,(Tern (v102,v3,v2)))
Tern (v102,(Tern (v1,v102,v2)),(Tern (v102,v3,v2))) = Tern (v1,v102,(Tern (v102,v3,v2))) by A504;
hence Tern ((Tern (v1,v102,v2)),(Tern (v102,v3,v2)),v102) = Tern (v1,v102,(Tern (v102,v3,v2))) by A3; :: thesis: verum
end;
A512: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v3,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v3,v2)))
Tern (v1,v3,v2) = Tern (v1,v2,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v3,v2))) by A509; :: thesis: verum
end;
A514: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v1,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern (v0,v1,(Tern (v1,v3,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v1,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern (v0,v1,(Tern (v1,v3,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v1) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) by A3;
hence Tern (v1,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern (v0,v1,(Tern (v1,v3,v2))) by A512; :: thesis: verum
end;
A517: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))) = Tern (v1,v0,(Tern (v0,v2,v3)))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))) = Tern (v1,v0,(Tern (v0,v2,v3)))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))) = Tern (v1,v0,(Tern (v0,v2,v3))) by A514; :: thesis: verum
end;
A520: for v1, v3, v2, v100 being Element of (BA2TBAA B) holds Tern (v1,v100,(Tern (v100,v2,v3))) = Tern (v100,(Tern (v100,v2,v3)),(Tern (v1,v100,v2)))
proof
let v1, v3, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v1,v100,(Tern (v100,v2,v3))) = Tern (v100,(Tern (v100,v2,v3)),(Tern (v1,v100,v2)))
Tern (v100,(Tern (v1,v100,v2)),(Tern (v100,v2,v3))) = Tern (v1,v100,(Tern (v100,v2,v3))) by A517;
hence Tern (v1,v100,(Tern (v100,v2,v3))) = Tern (v100,(Tern (v100,v2,v3)),(Tern (v1,v100,v2))) by A4; :: thesis: verum
end;
A526: for v104, v103, v101, v100, v1 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,(Tern (v100,(Tern (v1,v100,v101)),v104))))) = Tern (v1,v100,(Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,v104)))))
proof
let v104, v103, v101, v100, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,(Tern (v100,(Tern (v1,v100,v101)),v104))))) = Tern (v1,v100,(Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,v104)))))
Tern (v100,(Tern (v1,v100,v101)),(Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,v104))))) = Tern (v1,v100,(Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,v104))))) by A517;
hence Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,(Tern (v100,(Tern (v1,v100,v101)),v104))))) = Tern (v1,v100,(Tern (v100,v101,(Tern ((Tern (v1,v100,v101)),v103,v104))))) by A103; :: thesis: verum
end;
A529: for v4, v3, v0, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern ((Tern (v1,v2,v0)),v3,(Tern (v0,(Tern (v2,v0,v1)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
proof
let v4, v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern ((Tern (v1,v2,v0)),v3,(Tern (v0,(Tern (v2,v0,v1)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,v1,(Tern ((Tern (v1,v2,v0)),v3,(Tern (v0,(Tern (v2,v0,v1)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4))))) by A526; :: thesis: verum
end;
A531: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v2,v0,v1)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v2,v0,v1)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v2,v0,v1)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4))))) by A529; :: thesis: verum
end;
A533: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v1,v2,v0)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v1,v2,v0)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v1,v2,v0)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4))))) by A531; :: thesis: verum
end;
A535: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),v4))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4))))) by A533; :: thesis: verum
end;
A537: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
Tern (v0,(Tern (v0,v1,v2)),v4) = Tern (v0,v4,(Tern (v0,v1,v2))) by A4;
hence Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4))))) by A535; :: thesis: verum
end;
A539: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4)))))
Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) by A3;
hence Tern (v0,v1,(Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v2,v0,v1)),v3,v4))))) by A537; :: thesis: verum
end;
A542: for v3, v2, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v4,v0,(Tern (v0,v1,(Tern ((Tern (v4,v0,v1)),v2,v3)))))
proof
let v3, v2, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v4,v0,(Tern (v0,v1,(Tern ((Tern (v4,v0,v1)),v2,v3)))))
Tern (v2,(Tern (v0,v3,(Tern (v0,v1,v4)))),(Tern (v0,v1,v4))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v0,v1,v4))))) by A4;
hence Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v0,v1,v4))))))) = Tern (v4,v0,(Tern (v0,v1,(Tern ((Tern (v4,v0,v1)),v2,v3))))) by A539; :: thesis: verum
end;
A545: for v2, v4, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))) = Tern (v3,v0,(Tern (v0,v1,(Tern ((Tern (v3,v0,v1)),v2,v4)))))
proof
let v2, v4, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))) = Tern (v3,v0,(Tern (v0,v1,(Tern ((Tern (v3,v0,v1)),v2,v4)))))
Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v4,(Tern (v0,v1,v3))))))) = Tern (v0,(Tern (v0,v1,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))) by A451;
hence Tern (v0,(Tern (v0,v1,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))) = Tern (v3,v0,(Tern (v0,v1,(Tern ((Tern (v3,v0,v1)),v2,v4))))) by A542; :: thesis: verum
end;
A548: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v1,v2,v0)),v3,v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v1,v2,v0)),v3,v4)))))
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v1,v2,v0)),v3,v4))))) by A545; :: thesis: verum
end;
A550: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern ((Tern (v0,v1,v2)),v3,v4))))) by A548; :: thesis: verum
end;
A552: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v4,(Tern (v0,v1,v2)),v3)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v4,(Tern (v0,v1,v2)),v3)))))
Tern ((Tern (v0,v1,v2)),v3,v4) = Tern (v4,(Tern (v0,v1,v2)),v3) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v4,(Tern (v0,v1,v2)),v3))))) by A550; :: thesis: verum
end;
A554: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))
Tern (v4,(Tern (v0,v1,v2)),v3) = Tern (v3,v4,(Tern (v0,v1,v2))) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v2,v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A552; :: thesis: verum
end;
A556: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v2)
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v2)
Tern (v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v2) = Tern (v2,v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v2) by A554; :: thesis: verum
end;
A558: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))
Tern (v0,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A4;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A556; :: thesis: verum
end;
A561: for v101, v2, v104, v103 being Element of (BA2TBAA B) holds Tern ((Tern (v103,v104,v2)),v101,(Tern ((Tern (v103,v104,v2)),v103,(Tern (v103,v104,v2))))) = Tern (v103,(Tern (v103,v104,v2)),(Tern ((Tern (v103,v104,v2)),v103,(Tern ((Tern (v103,v104,v2)),v101,v104)))))
proof
let v101, v2, v104, v103 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v103,v104,v2)),v101,(Tern ((Tern (v103,v104,v2)),v103,(Tern (v103,v104,v2))))) = Tern (v103,(Tern (v103,v104,v2)),(Tern ((Tern (v103,v104,v2)),v103,(Tern ((Tern (v103,v104,v2)),v101,v104)))))
Tern (v103,(Tern (v103,v104,v2)),(Tern ((Tern (v103,v104,v2)),v103,v104))) = Tern ((Tern (v103,v104,v2)),v103,(Tern (v103,v104,v2))) by A520;
hence Tern ((Tern (v103,v104,v2)),v101,(Tern ((Tern (v103,v104,v2)),v103,(Tern (v103,v104,v2))))) = Tern (v103,(Tern (v103,v104,v2)),(Tern ((Tern (v103,v104,v2)),v103,(Tern ((Tern (v103,v104,v2)),v101,v104))))) by A162; :: thesis: verum
end;
A564: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1)))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1))))) by A561; :: thesis: verum
end;
A566: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1)))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A34;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1))))) by A564; :: thesis: verum
end;
A568: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1)))))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v1))))) by A566; :: thesis: verum
end;
A571: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,v3) = Tern (v1,(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v2)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,v3) = Tern (v1,(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v2)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A34;
hence Tern (v1,v2,v3) = Tern (v1,(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v2))))) by A568; :: thesis: verum
end;
A574: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,(Tern (v0,v1,v2)),v3)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,(Tern (v0,v1,v2)),v3)))))
Tern ((Tern (v0,v1,v2)),v3,v1) = Tern (v1,(Tern (v0,v1,v2)),v3) by A3;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,(Tern (v0,v1,v2)),v3))))) by A571; :: thesis: verum
end;
A576: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,v3,(Tern (v0,v1,v2)))))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,v3,(Tern (v0,v1,v2)))))))
Tern (v1,(Tern (v0,v1,v2)),v3) = Tern (v1,v3,(Tern (v0,v1,v2))) by A4;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,v3,(Tern (v0,v1,v2))))))) by A574; :: thesis: verum
end;
A578: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v1,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v1,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v1,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v1,v3,(Tern (v0,v1,v2))))) by A3;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v1,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))))) by A576; :: thesis: verum
end;
A580: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2)))))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2)))))))
Tern (v0,(Tern (v1,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))) by A4;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))))) by A578; :: thesis: verum
end;
A582: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2)))))))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2)))))))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))))) by A558;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))))))) by A580; :: thesis: verum
end;
A584: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,v2)))))))
proof
let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,v2)))))))
Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))) = Tern (v0,v1,(Tern (v1,v3,v2))) by A111;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,v2))))))) by A582; :: thesis: verum
end;
A586: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))))
Tern (v1,v3,v2) = Tern (v1,v2,v3) by A4;
hence Tern (v0,v1,v2) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))))) by A584; :: thesis: verum
end;
A588: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2)))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2))))) by A193;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2))))) by A586; :: thesis: verum
end;
A590: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))))))
Tern (v0,(Tern (v0,v1,(Tern (v1,v2,v3)))),v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A4;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))))))) by A588; :: thesis: verum
end;
A592: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))))
Tern (v0,v2,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A74;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))))) by A590; :: thesis: verum
end;
A594: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3)))))
Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A89;
hence Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A592; :: thesis: verum
end;
A599: for v102, v3, v100, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v2,(Tern (v2,v100,v3)))),v102) = Tern (v102,v2,v100)
proof
let v102, v3, v100, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v2,(Tern (v2,v100,v3)))),v102) = Tern (v102,v2,v100)
Tern (v102,v100,(Tern (v102,v2,(Tern (v2,v100,v3))))) = Tern (v102,v2,v100) by A594;
hence Tern (v100,(Tern (v102,v2,(Tern (v2,v100,v3)))),v102) = Tern (v102,v2,v100) by A3; :: thesis: verum
end;
A602: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v2)))),v1) = Tern (v1,v2,v0)
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v2)))),v1) = Tern (v1,v2,v0)
Tern (v0,v3,v2) = Tern (v2,v0,v3) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v2)))),v1) = Tern (v1,v2,v0) by A599; :: thesis: verum
end;
A604: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v1) = Tern (v1,v2,v0)
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v1) = Tern (v1,v2,v0)
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v1) = Tern (v1,v2,v0) by A602; :: thesis: verum
end;
A606: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v1,v2,v0)
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v1,v2,v0)
Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),v1) = Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A4;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v1,v2,v0) by A604; :: thesis: verum
end;
A608: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v0,v1,v2)
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v0,v1,v2)
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern (v0,v1,v2) by A606; :: thesis: verum
end;
A610: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v2,v1)
proof
let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v2,v1)
Tern (v2,v1,v3) = Tern (v3,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v2,v1) by A594; :: thesis: verum
end;
A612: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v2,v1)
proof
let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v2,v1)
Tern (v3,v2,v1) = Tern (v1,v3,v2) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v2,v1) by A610; :: thesis: verum
end;
A614: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v2,v1)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v2,v1)
Tern (v1,v3,v2) = Tern (v1,v2,v3) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v2,v1) by A612; :: thesis: verum
end;
A616: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v1,v2)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v1,v2)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v1,v2) by A614; :: thesis: verum
end;
A619: for v101, v100, v3, v102, v2 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,(Tern (v2,v102,v3)))))))
proof
let v101, v100, v3, v102, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,(Tern (v2,v102,v3)))))))
Tern (v100,v102,(Tern (v100,v2,(Tern (v2,v102,v3))))) = Tern (v100,v2,v102) by A594;
hence Tern (v100,v101,(Tern (v100,v2,v102))) = Tern (v100,v102,(Tern (v100,v101,(Tern (v100,v2,(Tern (v2,v102,v3))))))) by A27; :: thesis: verum
end;
A625: for v100, v2, v3, v101, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v102,(Tern (v102,v2,(Tern (v102,v101,v3))))))) = Tern (v100,v102,v101)
proof
let v100, v2, v3, v101, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v102,(Tern (v102,v2,(Tern (v102,v101,v3))))))) = Tern (v100,v102,v101)
Tern (v102,v101,(Tern (v102,v2,v3))) = Tern (v102,v2,(Tern (v102,v101,v3))) by A27;
hence Tern (v100,v101,(Tern (v100,v102,(Tern (v102,v2,(Tern (v102,v101,v3))))))) = Tern (v100,v102,v101) by A594; :: thesis: verum
end;
A628: for v0, v3, v2, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v4,v2))))))) = Tern (v0,v2,v1)
proof
let v0, v3, v2, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v4,v2))))))) = Tern (v0,v2,v1)
Tern (v1,v4,v2) = Tern (v2,v1,v4) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v4,v2))))))) = Tern (v0,v2,v1) by A625; :: thesis: verum
end;
A630: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v0,v2,v1)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v0,v2,v1)
Tern (v1,v4,v2) = Tern (v1,v2,v4) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v0,v2,v1) by A628; :: thesis: verum
end;
A632: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v0,v1,v2)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v0,v1,v2)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v0,v1,v2) by A630; :: thesis: verum
end;
A635: for v100, v103, v3, v1, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v1,v3)),(Tern (v100,v102,(Tern (v102,(Tern (v102,v1,v3)),v103))))) = Tern (v102,v1,(Tern (v100,v102,v3)))
proof
let v100, v103, v3, v1, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v1,v3)),(Tern (v100,v102,(Tern (v102,(Tern (v102,v1,v3)),v103))))) = Tern (v102,v1,(Tern (v100,v102,v3)))
Tern (v102,v1,(Tern (v100,v102,v3))) = Tern (v100,v102,(Tern (v102,v1,v3))) by A45;
hence Tern (v100,(Tern (v102,v1,v3)),(Tern (v100,v102,(Tern (v102,(Tern (v102,v1,v3)),v103))))) = Tern (v102,v1,(Tern (v100,v102,v3))) by A594; :: thesis: verum
end;
A638: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v1,v3)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v1,v3)))
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v1,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v1,v3))) by A635; :: thesis: verum
end;
A640: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern (v1,v2,(Tern (v0,v1,v3)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern (v1,v2,(Tern (v0,v1,v3)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) by A492;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern (v1,v2,(Tern (v0,v1,v3))) by A638; :: thesis: verum
end;
A643: for v2, v0, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v3,(Tern (v0,v1,v4)))
proof
let v2, v0, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v3,(Tern (v0,v1,v4)))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v3,v4))) = Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v3,(Tern (v0,v1,v4))) by A640; :: thesis: verum
end;
A647: for v100, v103, v3, v102, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v102,v3)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v102,v3)),v103))))) = Tern (v2,v102,(Tern (v100,v102,v3)))
proof
let v100, v103, v3, v102, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v102,v3)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v102,v3)),v103))))) = Tern (v2,v102,(Tern (v100,v102,v3)))
Tern (v100,v102,(Tern (v2,v102,v3))) = Tern (v2,v102,(Tern (v100,v102,v3))) by A100;
hence Tern (v100,(Tern (v2,v102,v3)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v102,v3)),v103))))) = Tern (v2,v102,(Tern (v100,v102,v3))) by A594; :: thesis: verum
end;
A650: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v2,v3)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v2,v3)))
Tern (v2,(Tern (v1,v2,v3)),v4) = Tern (v2,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v2,v3))) by A647; :: thesis: verum
end;
A652: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v1))))) = Tern (v0,v2,v1)
proof
let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v1))))) = Tern (v0,v2,v1)
Tern (v2,v3,(Tern (v0,v2,v1))) = Tern (v0,v2,(Tern (v2,v1,v3))) by A134;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v1))))) = Tern (v0,v2,v1) by A594; :: thesis: verum
end;
A654: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v2))))) = Tern (v0,v2,v1)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v2))))) = Tern (v0,v2,v1)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v2))))) = Tern (v0,v2,v1) by A652; :: thesis: verum
end;
A656: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v2))))) = Tern (v0,v1,v2)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v2))))) = Tern (v0,v1,v2)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v2))))) = Tern (v0,v1,v2) by A654; :: thesis: verum
end;
A659: for v100, v103, v1, v3, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v3,v1)),(Tern (v100,v102,(Tern (v102,(Tern (v102,v3,v1)),v103))))) = Tern (v102,v1,(Tern (v100,v102,v3)))
proof
let v100, v103, v1, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v3,v1)),(Tern (v100,v102,(Tern (v102,(Tern (v102,v3,v1)),v103))))) = Tern (v102,v1,(Tern (v100,v102,v3)))
Tern (v102,v1,(Tern (v100,v102,v3))) = Tern (v100,v102,(Tern (v102,v3,v1))) by A134;
hence Tern (v100,(Tern (v102,v3,v1)),(Tern (v100,v102,(Tern (v102,(Tern (v102,v3,v1)),v103))))) = Tern (v102,v1,(Tern (v100,v102,v3))) by A594; :: thesis: verum
end;
A662: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v1,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A659; :: thesis: verum
end;
A664: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) by A492;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A662; :: thesis: verum
end;
A667: for v2, v0, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v4,(Tern (v0,v1,v3)))
proof
let v2, v0, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v4,(Tern (v0,v1,v3)))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v3,v4))) = Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v4,(Tern (v0,v1,v3))) by A664; :: thesis: verum
end;
A670: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
now :: thesis: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v1,v3))) by A643;
hence Tern (v1,v2,(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A667; :: thesis: verum
end;
hence for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2))) ; :: thesis: verum
end;
A674: for v101, v100, v3, v102, v103 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v103,v102))) = Tern (v100,(Tern (v103,v102,v3)),(Tern (v100,v101,(Tern (v100,v102,v103)))))
proof
let v101, v100, v3, v102, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v103,v102))) = Tern (v100,(Tern (v103,v102,v3)),(Tern (v100,v101,(Tern (v100,v102,v103)))))
Tern (v100,v102,(Tern (v100,v103,(Tern (v103,v102,v3))))) = Tern (v100,v103,v102) by A594;
hence Tern (v100,v101,(Tern (v100,v103,v102))) = Tern (v100,(Tern (v103,v102,v3)),(Tern (v100,v101,(Tern (v100,v102,v103))))) by A145; :: thesis: verum
end;
A677: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v0,v2,v3)))))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v0,v2,v3)))))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,v1,(Tern (v0,v2,v3))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v0,v2,v3))))) by A674; :: thesis: verum
end;
A681: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3)))))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3))))) by A469; :: thesis: verum
end;
A683: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) by A492;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3))))) by A681; :: thesis: verum
end;
A685: for v2, v3, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3)))))
proof
let v2, v3, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3)))))
Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v1,v2) by A616;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v1,v0,v3))))) by A683; :: thesis: verum
end;
A687: for v2, v1, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v0,v3,v1)))))
proof
let v2, v1, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v0,v3,v1)))))
Tern (v0,v3,v1) = Tern (v1,v0,v3) by A3;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v0,v3,v1))))) by A685; :: thesis: verum
end;
A689: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v0,v1,v3)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v0,v1,v3)))))
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v2,v0,(Tern (v0,v1,v3))))) by A687; :: thesis: verum
end;
A691: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,(Tern (v0,v1,v3)),v2)))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,(Tern (v0,v1,v3)),v2)))
Tern (v0,(Tern (v0,v1,v3)),v2) = Tern (v2,v0,(Tern (v0,v1,v3))) by A3;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,(Tern (v0,v1,v3)),v2))) by A689; :: thesis: verum
end;
A693: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v2,(Tern (v0,v1,v3)))))
Tern (v0,(Tern (v0,v1,v3)),v2) = Tern (v0,v2,(Tern (v0,v1,v3))) by A4;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v2,(Tern (v0,v1,v3))))) by A691; :: thesis: verum
end;
A697: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3)))))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3)))))
Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))))) = Tern (v0,v1,v2) by A656;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A487; :: thesis: verum
end;
A702: for v100, v3, v102, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v102,v3)),v102) = Tern (v102,v3,(Tern (v2,v102,v100)))
proof
let v100, v3, v102, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v102,v3)),v102) = Tern (v102,v3,(Tern (v2,v102,v100)))
Tern (v102,v100,(Tern (v2,v102,v3))) = Tern (v102,v3,(Tern (v2,v102,v100))) by A670;
hence Tern (v100,(Tern (v2,v102,v3)),v102) = Tern (v102,v3,(Tern (v2,v102,v100))) by A3; :: thesis: verum
end;
A705: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v1,v2,v3))) = Tern (v2,v3,(Tern (v1,v2,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v1,v2,v3))) = Tern (v2,v3,(Tern (v1,v2,v0)))
Tern (v0,(Tern (v1,v2,v3)),v2) = Tern (v0,v2,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v2,(Tern (v1,v2,v3))) = Tern (v2,v3,(Tern (v1,v2,v0))) by A702; :: thesis: verum
end;
A708: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v1,v3,(Tern (v0,v2,v1)))
proof
let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v1,v3,(Tern (v0,v2,v1)))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v1,v3,(Tern (v0,v2,v1))) by A705; :: thesis: verum
end;
A713: for v100, v102, v3, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,v102)),v102) = Tern (v2,v102,(Tern (v3,v102,v100)))
proof
let v100, v102, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,v102)),v102) = Tern (v2,v102,(Tern (v3,v102,v100)))
Tern (v102,v100,(Tern (v2,v3,v102))) = Tern (v2,v102,(Tern (v3,v102,v100))) by A708;
hence Tern (v100,(Tern (v2,v3,v102)),v102) = Tern (v2,v102,(Tern (v3,v102,v100))) by A3; :: thesis: verum
end;
A716: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v2,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v2,v3,v0)))
Tern (v0,(Tern (v1,v2,v3)),v3) = Tern (v0,v3,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v3,(Tern (v1,v2,v3))) = Tern (v1,v3,(Tern (v2,v3,v0))) by A713; :: thesis: verum
end;
A719: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v2,v1,(Tern (v0,v3,v1)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v2,v1,(Tern (v0,v3,v1)))
Tern (v3,v1,v0) = Tern (v0,v3,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v2,v1,(Tern (v0,v3,v1))) by A716; :: thesis: verum
end;
A722: for v100, v103, v102, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v102,v101))) = Tern (v102,(Tern (v100,v101,v103)),(Tern (v100,v101,v102)))
proof
let v100, v103, v102, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v102,v101))) = Tern (v102,(Tern (v100,v101,v103)),(Tern (v100,v101,v102)))
Tern (v102,(Tern (v100,v101,v103)),(Tern (v100,v101,v102))) = Tern (v100,v102,(Tern (v101,v102,(Tern (v100,v101,v103))))) by A708;
hence Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v102,v101))) = Tern (v102,(Tern (v100,v101,v103)),(Tern (v100,v101,v102))) by A149; :: thesis: verum
end;
A725: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A722; :: thesis: verum
end;
A727: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) by A492;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A725; :: thesis: verum
end;
A729: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v1,v2) by A616;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A727; :: thesis: verum
end;
A734: for v100, v103, v1, v102, v3 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v3,v102,v1)),(Tern (v100,v102,(Tern (v102,(Tern (v3,v102,v1)),v103))))) = Tern (v102,v1,(Tern (v100,v3,v102)))
proof
let v100, v103, v1, v102, v3 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v3,v102,v1)),(Tern (v100,v102,(Tern (v102,(Tern (v3,v102,v1)),v103))))) = Tern (v102,v1,(Tern (v100,v3,v102)))
Tern (v102,v1,(Tern (v100,v3,v102))) = Tern (v100,v102,(Tern (v3,v102,v1))) by A708;
hence Tern (v100,(Tern (v3,v102,v1)),(Tern (v100,v102,(Tern (v102,(Tern (v3,v102,v1)),v103))))) = Tern (v102,v1,(Tern (v100,v3,v102))) by A594; :: thesis: verum
end;
A737: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v2,v3,(Tern (v0,v1,v2)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v2,v3,(Tern (v0,v1,v2)))
Tern (v2,(Tern (v1,v2,v3)),v4) = Tern (v2,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v2,v3,(Tern (v0,v1,v2))) by A734; :: thesis: verum
end;
A739: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v2)))
proof
now :: thesis: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v2)))
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v2,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v2,(Tern (v0,v2,v3))) by A650;
hence Tern (v1,v2,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v2))) by A737; :: thesis: verum
end;
hence for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v2))) ; :: thesis: verum
end;
A745: for v100, v2, v103, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v103,v2)),(Tern (v102,v103,v2))) = Tern (v102,(Tern (v102,v103,v2)),(Tern (v100,v103,(Tern (v102,v103,v2)))))
proof
let v100, v2, v103, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v103,v2)),(Tern (v102,v103,v2))) = Tern (v102,(Tern (v102,v103,v2)),(Tern (v100,v103,(Tern (v102,v103,v2)))))
Tern (v102,v103,(Tern (v102,v103,v2))) = Tern (v102,v103,v2) by A74;
hence Tern (v100,(Tern (v102,v103,v2)),(Tern (v102,v103,v2))) = Tern (v102,(Tern (v102,v103,v2)),(Tern (v100,v103,(Tern (v102,v103,v2))))) by A719; :: thesis: verum
end;
A748: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,v3) = Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,v3) = Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A34;
hence Tern (v1,v2,v3) = Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3))))) by A745; :: thesis: verum
end;
A751: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v1,(Tern (v0,v1,v2)))))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v1,(Tern (v0,v1,v2)))))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v1,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v1,(Tern (v0,v1,v2))))))) by A558;
hence Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v1,(Tern (v0,v1,v2))))))) by A748; :: thesis: verum
end;
A753: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v3,v1,(Tern (v0,v1,v2)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v3,v1,(Tern (v0,v1,v2)))))
Tern (v0,v1,(Tern (v3,v1,(Tern (v0,v1,v2))))) = Tern (v3,v1,(Tern (v0,v1,v2))) by A311;
hence Tern (v0,v1,v2) = Tern (v0,v2,(Tern (v3,v1,(Tern (v0,v1,v2))))) by A751; :: thesis: verum
end;
A758: for v102, v100, v1, v3, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v3,v1)),(Tern (v102,v103,(Tern (v103,v3,v1))))) = Tern (v102,(Tern (v103,v3,v1)),(Tern (v103,v1,(Tern (v100,v103,v3)))))
proof
let v102, v100, v1, v3, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v103,v3,v1)),(Tern (v102,v103,(Tern (v103,v3,v1))))) = Tern (v102,(Tern (v103,v3,v1)),(Tern (v103,v1,(Tern (v100,v103,v3)))))
Tern (v103,v1,(Tern (v100,v103,v3))) = Tern (v100,v103,(Tern (v103,v3,v1))) by A134;
hence Tern (v100,(Tern (v103,v3,v1)),(Tern (v102,v103,(Tern (v103,v3,v1))))) = Tern (v102,(Tern (v103,v3,v1)),(Tern (v103,v1,(Tern (v100,v103,v3))))) by A719; :: thesis: verum
end;
A761: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v4))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v4))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2)))))
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v4,v1,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v4))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2))))) by A758; :: thesis: verum
end;
A763: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2)))))
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v1,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2))))) by A761; :: thesis: verum
end;
A766: for v102, v104, v103, v100 being Element of (BA2TBAA B) holds Tern (v102,(Tern (v100,v103,v104)),(Tern (v100,v103,(Tern (v100,v103,v104))))) = Tern (v100,v103,(Tern (v100,(Tern (v100,v103,v104)),(Tern (v102,v103,v104)))))
proof
let v102, v104, v103, v100 be Element of (BA2TBAA B); :: thesis: Tern (v102,(Tern (v100,v103,v104)),(Tern (v100,v103,(Tern (v100,v103,v104))))) = Tern (v100,v103,(Tern (v100,(Tern (v100,v103,v104)),(Tern (v102,v103,v104)))))
Tern (v100,(Tern (v100,v103,v104)),(Tern (v102,v103,(Tern (v100,v103,v104))))) = Tern (v102,(Tern (v100,v103,v104)),(Tern (v100,v103,(Tern (v100,v103,v104))))) by A719;
hence Tern (v102,(Tern (v100,v103,v104)),(Tern (v100,v103,(Tern (v100,v103,v104))))) = Tern (v100,v103,(Tern (v100,(Tern (v100,v103,v104)),(Tern (v102,v103,v104))))) by A124; :: thesis: verum
end;
A769: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,v3)))))
Tern (v1,v2,(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A74;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))))) by A766; :: thesis: verum
end;
A771: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,v3) = Tern (v1,v2,(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,v3) = Tern (v1,v2,(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A34;
hence Tern (v1,v2,v3) = Tern (v1,v2,(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))))) by A769; :: thesis: verum
end;
A776: for v103, v3, v100, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v100,v3)),(Tern (v102,v103,(Tern (v102,v100,v3))))) = Tern (v102,(Tern (v100,v103,v3)),(Tern (v102,(Tern (v102,v100,v3)),v100)))
proof
let v103, v3, v100, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v100,v3)),(Tern (v102,v103,(Tern (v102,v100,v3))))) = Tern (v102,(Tern (v100,v103,v3)),(Tern (v102,(Tern (v102,v100,v3)),v100)))
Tern (v102,(Tern (v100,v103,v3)),(Tern (v102,(Tern (v102,v100,v3)),v100))) = Tern (v102,(Tern (v102,v100,v3)),(Tern (v100,v103,(Tern (v102,v100,v3))))) by A149;
hence Tern (v100,(Tern (v102,v100,v3)),(Tern (v102,v103,(Tern (v102,v100,v3))))) = Tern (v102,(Tern (v100,v103,v3)),(Tern (v102,(Tern (v102,v100,v3)),v100))) by A719; :: thesis: verum
end;
A779: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v2,v1)),(Tern (v1,v3,(Tern (v1,v0,v2))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v2,v1)),(Tern (v1,v3,(Tern (v1,v0,v2))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,(Tern (v0,v2,v1)),(Tern (v1,v3,(Tern (v1,v0,v2))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0))) by A776; :: thesis: verum
end;
A782: for v3, v1, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v2,v1)),(Tern (v2,v3,(Tern (v2,v0,v1))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
proof
let v3, v1, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v2,v1)),(Tern (v2,v3,(Tern (v2,v0,v1))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
Tern (v0,v1,v2) = Tern (v0,v2,v1) by A4;
hence Tern (v0,(Tern (v0,v2,v1)),(Tern (v2,v3,(Tern (v2,v0,v1))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0))) by A779; :: thesis: verum
end;
A785: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v2,v1))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
proof
let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v2,v1))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v2,v1))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0))) by A782; :: thesis: verum
end;
A787: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0))) by A785; :: thesis: verum
end;
A789: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))))) by A558;
hence Tern (v0,v2,(Tern (v0,v1,(Tern (v1,v3,(Tern (v0,v1,v2))))))) = Tern (v1,(Tern (v0,v3,v2)),(Tern (v1,(Tern (v1,v0,v2)),v0))) by A787; :: thesis: verum
end;
A792: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,v1))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,v1))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
Tern (v0,v2,(Tern (v2,v3,(Tern (v0,v2,v1))))) = Tern (v0,v2,(Tern (v2,v3,v1))) by A111;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v3,v1))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0))) by A789; :: thesis: verum
end;
A794: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v1,v3))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
proof
let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v1,v3))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
Tern (v2,v3,v1) = Tern (v2,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v1,v3))))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0))) by A792; :: thesis: verum
end;
A796: for v2, v1, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v2,v1) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
proof
let v2, v1, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,v1) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0)))
Tern (v0,v1,(Tern (v0,v2,(Tern (v2,v1,v3))))) = Tern (v0,v2,v1) by A594;
hence Tern (v0,v2,v1) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v2,v0,v1)),v0))) by A794; :: thesis: verum
end;
A799: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v1,v0,v2)),v0)))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v1,v0,v2)),v0))) by A796; :: thesis: verum
end;
A801: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v0,v2,v1)),v0)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v0,v2,v1)),v0)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v0,v2,v1)),v0))) by A799; :: thesis: verum
end;
A803: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v0,v1,v2)),v0)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v0,v1,v2)),v0)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v1,(Tern (v0,v1,v2)),v0))) by A801; :: thesis: verum
end;
A805: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v0,v1,(Tern (v0,v1,v2)))))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v0,v1,(Tern (v0,v1,v2)))))
Tern (v1,(Tern (v0,v1,v2)),v0) = Tern (v0,v1,(Tern (v0,v1,v2))) by A3;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v0,v1,(Tern (v0,v1,v2))))) by A803; :: thesis: verum
end;
A807: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v0,v1,v2)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v0,v1,v2)))
Tern (v0,v1,(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A74;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v3)),(Tern (v0,v1,v2))) by A805; :: thesis: verum
end;
A812: for v100, v103, v102, v3, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,v102)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v3,v102)),v103))))) = Tern (v2,v102,(Tern (v100,v3,v102)))
proof
let v100, v103, v102, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,v102)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v3,v102)),v103))))) = Tern (v2,v102,(Tern (v100,v3,v102)))
Tern (v100,v102,(Tern (v2,v3,v102))) = Tern (v2,v102,(Tern (v100,v3,v102))) by A719;
hence Tern (v100,(Tern (v2,v3,v102)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v3,v102)),v103))))) = Tern (v2,v102,(Tern (v100,v3,v102))) by A594; :: thesis: verum
end;
A815: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v2,v3)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v2,v3)))
Tern (v3,(Tern (v1,v2,v3)),v4) = Tern (v3,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v2,v3))) by A812; :: thesis: verum
end;
A817: for v0, v2, v1, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v3,v1,v2)),(Tern (v1,v2,v0))) = Tern (v1,v2,v0)
proof
let v0, v2, v1, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v3,v1,v2)),(Tern (v1,v2,v0))) = Tern (v1,v2,v0)
Tern (v1,v2,v3) = Tern (v3,v1,v2) by A3;
hence Tern (v0,(Tern (v3,v1,v2)),(Tern (v1,v2,v0))) = Tern (v1,v2,v0) by A729; :: thesis: verum
end;
A820: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v2,v3,v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v2,v3,v0)
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v2,v3,v0) by A817; :: thesis: verum
end;
A822: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3)
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3) by A820; :: thesis: verum
end;
A824: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v3,v1)),(Tern (v1,v2,v0))) = Tern (v1,v2,v0)
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v2,v3,v1)),(Tern (v1,v2,v0))) = Tern (v1,v2,v0)
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern (v0,(Tern (v2,v3,v1)),(Tern (v1,v2,v0))) = Tern (v1,v2,v0) by A729; :: thesis: verum
end;
A827: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v1))) = Tern (v3,v1,v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v1))) = Tern (v3,v1,v0)
Tern (v3,v1,v0) = Tern (v0,v3,v1) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v1))) = Tern (v3,v1,v0) by A824; :: thesis: verum
end;
A829: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v3))) = Tern (v3,v1,v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v3))) = Tern (v3,v1,v0)
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v3))) = Tern (v3,v1,v0) by A827; :: thesis: verum
end;
A831: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v3,(Tern (v1,v2,v3))))) = Tern (v3,v1,v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v3,(Tern (v1,v2,v3))))) = Tern (v3,v1,v0)
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v3))) = Tern (v0,v1,(Tern (v0,v3,(Tern (v1,v2,v3))))) by A492;
hence Tern (v0,v1,(Tern (v0,v3,(Tern (v1,v2,v3))))) = Tern (v3,v1,v0) by A829; :: thesis: verum
end;
A834: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v2,v1)
proof
let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v2,v1)
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v2,v1) by A831; :: thesis: verum
end;
A836: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v1,v2)
proof
let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v1,v2)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v2))))) = Tern (v0,v1,v2) by A834; :: thesis: verum
end;
A839: for v3, v100, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,v100) = Tern (v100,(Tern (v1,v2,v100)),(Tern (v1,v2,v3)))
proof
let v3, v100, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,v100) = Tern (v100,(Tern (v1,v2,v100)),(Tern (v1,v2,v3)))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v1,v2,v100))) = Tern (v1,v2,v100) by A729;
hence Tern (v1,v2,v100) = Tern (v100,(Tern (v1,v2,v100)),(Tern (v1,v2,v3))) by A4; :: thesis: verum
end;
A845: for v100, v2, v3, v102, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v101,(Tern (v101,v102,v3)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
proof
let v100, v2, v3, v102, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v101,(Tern (v101,v102,v3)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
Tern (v101,v102,(Tern (v2,v101,v3))) = Tern (v2,v101,(Tern (v101,v102,v3))) by A45;
hence Tern (v100,(Tern (v2,v101,(Tern (v101,v102,v3)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100) by A729; :: thesis: verum
end;
A848: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v2,v3,v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v2,v3,v0)
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v2,v3,v0) by A845; :: thesis: verum
end;
A850: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v2,v3)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v2,v3)
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v2,v3) by A848; :: thesis: verum
end;
A853: for v100, v1, v102, v2, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v1,(Tern (v101,v2,v102)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
proof
let v100, v1, v102, v2, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v1,(Tern (v101,v2,v102)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
Tern (v101,v1,(Tern (v101,v2,v102))) = Tern (v101,v102,(Tern (v101,v1,v2))) by A55;
hence Tern (v100,(Tern (v101,v1,(Tern (v101,v2,v102)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100) by A729; :: thesis: verum
end;
A856: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v0,v1,v4))) = Tern (v1,v4,v0)
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v0,v1,v4))) = Tern (v1,v4,v0)
Tern (v1,v4,v0) = Tern (v0,v1,v4) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v0,v1,v4))) = Tern (v1,v4,v0) by A853; :: thesis: verum
end;
A858: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v4,v0)
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v4,v0)
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v0,v1,v4))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v4))))))) by A492;
hence Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v1,v4,v0) by A856; :: thesis: verum
end;
A861: for v0, v3, v2, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,(Tern (v1,v4,v2))))))) = Tern (v0,v1,v2)
proof
let v0, v3, v2, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,(Tern (v1,v4,v2))))))) = Tern (v0,v1,v2)
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,(Tern (v1,v4,v2))))))) = Tern (v0,v1,v2) by A858; :: thesis: verum
end;
A864: for v100, v2, v102, v3, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v101,(Tern (v101,v3,v102)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
proof
let v100, v2, v102, v3, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v101,(Tern (v101,v3,v102)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
Tern (v101,v102,(Tern (v2,v101,v3))) = Tern (v2,v101,(Tern (v101,v3,v102))) by A134;
hence Tern (v100,(Tern (v2,v101,(Tern (v101,v3,v102)))),(Tern (v101,v102,v100))) = Tern (v101,v102,v100) by A729; :: thesis: verum
end;
A867: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) = Tern (v2,v4,v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) = Tern (v2,v4,v0)
Tern (v2,v4,v0) = Tern (v0,v2,v4) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) = Tern (v2,v4,v0) by A864; :: thesis: verum
end;
A869: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) = Tern (v0,v2,v4)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) = Tern (v0,v2,v4)
Tern (v2,v4,v0) = Tern (v0,v2,v4) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) = Tern (v0,v2,v4) by A867; :: thesis: verum
end;
A872: for v102, v100, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v102,(Tern (v1,v2,v102))))) = Tern (v100,v102,(Tern (v1,v2,v3)))
proof
let v102, v100, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v102,(Tern (v1,v2,v102))))) = Tern (v100,v102,(Tern (v1,v2,v3)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v1,v2,v102))) = Tern (v1,v2,v102) by A729;
hence Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v102,(Tern (v1,v2,v102))))) = Tern (v100,v102,(Tern (v1,v2,v3))) by A594; :: thesis: verum
end;
A876: for v103, v102, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v102)),(Tern (v102,(Tern (v1,v2,v3)),v103))) = Tern ((Tern (v1,v2,v3)),v103,(Tern (v1,v2,v102)))
proof
let v103, v102, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v102)),(Tern (v102,(Tern (v1,v2,v3)),v103))) = Tern ((Tern (v1,v2,v3)),v103,(Tern (v1,v2,v102)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v1,v2,v102))) = Tern (v1,v2,v102) by A729;
hence Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v102)),(Tern (v102,(Tern (v1,v2,v3)),v103))) = Tern ((Tern (v1,v2,v3)),v103,(Tern (v1,v2,v102))) by A670; :: thesis: verum
end;
A879: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v0,v1,v3)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v0,v1,v3)))
Tern (v3,(Tern (v0,v1,v2)),v4) = Tern (v3,v4,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v0,v1,v3))) by A876; :: thesis: verum
end;
A881: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v0,v1,v3))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A879; :: thesis: verum
end;
A884: for v100, v101, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v2,v101)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100)
proof
let v100, v101, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v2,v101)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100)
Tern (v101,(Tern (v1,v2,v3)),(Tern (v1,v2,v101))) = Tern (v1,v2,v101) by A729;
hence Tern (v100,(Tern (v1,v2,v101)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100) by A729; :: thesis: verum
end;
A887: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v1,v2,v4))))) = Tern (v3,(Tern (v1,v2,v4)),v0)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v1,v2,v4))))) = Tern (v3,(Tern (v1,v2,v4)),v0)
Tern (v3,(Tern (v1,v2,v4)),v0) = Tern (v0,v3,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v1,v2,v4))))) = Tern (v3,(Tern (v1,v2,v4)),v0) by A884; :: thesis: verum
end;
A889: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v1,v2,v4))))) = Tern (v0,v3,(Tern (v1,v2,v4)))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v1,v2,v4))))) = Tern (v0,v3,(Tern (v1,v2,v4)))
Tern (v3,(Tern (v1,v2,v4)),v0) = Tern (v0,v3,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v1,v2,v4))))) = Tern (v0,v3,(Tern (v1,v2,v4))) by A887; :: thesis: verum
end;
A892: for v100, v102, v3, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,v102)),v102) = Tern (v3,v102,(Tern (v2,v102,v100)))
proof
let v100, v102, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,v102)),v102) = Tern (v3,v102,(Tern (v2,v102,v100)))
Tern (v102,v100,(Tern (v2,v3,v102))) = Tern (v3,v102,(Tern (v2,v102,v100))) by A739;
hence Tern (v100,(Tern (v2,v3,v102)),v102) = Tern (v3,v102,(Tern (v2,v102,v100))) by A3; :: thesis: verum
end;
A895: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v1,v2,v3))) = Tern (v2,v3,(Tern (v1,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v1,v2,v3))) = Tern (v2,v3,(Tern (v1,v3,v0)))
Tern (v0,(Tern (v1,v2,v3)),v3) = Tern (v0,v3,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v3,(Tern (v1,v2,v3))) = Tern (v2,v3,(Tern (v1,v3,v0))) by A892; :: thesis: verum
end;
A898: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v3,v1,(Tern (v0,v2,v1)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v3,v1,(Tern (v0,v2,v1)))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v3,v1,(Tern (v0,v2,v1))) by A895; :: thesis: verum
end;
A901: for v101, v103, v2, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v102,v2,v103)),v101,(Tern (v102,v2,v103))) = Tern (v103,(Tern (v102,v2,v103)),(Tern (v102,(Tern (v102,v2,v103)),v101)))
proof
let v101, v103, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v102,v2,v103)),v101,(Tern (v102,v2,v103))) = Tern (v103,(Tern (v102,v2,v103)),(Tern (v102,(Tern (v102,v2,v103)),v101)))
Tern (v102,v103,(Tern (v102,v2,v103))) = Tern (v102,v2,v103) by A63;
hence Tern ((Tern (v102,v2,v103)),v101,(Tern (v102,v2,v103))) = Tern (v103,(Tern (v102,v2,v103)),(Tern (v102,(Tern (v102,v2,v103)),v101))) by A739; :: thesis: verum
end;
A904: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v3)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v3)))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v3))) by A901; :: thesis: verum
end;
A907: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,v3) = Tern (v3,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,v3) = Tern (v3,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v0)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A34;
hence Tern (v1,v2,v3) = Tern (v3,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v0))) by A904; :: thesis: verum
end;
A910: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v0,v1,v2)),v3) = Tern (v0,v3,(Tern (v0,v1,v2))) by A4;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2))))) by A907; :: thesis: verum
end;
A915: for v103, v100, v102, v3, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,v102)),(Tern (v102,v100,v103))) = Tern (v100,v103,(Tern (v3,v102,(Tern (v2,v102,v100)))))
proof
let v103, v100, v102, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,v102)),(Tern (v102,v100,v103))) = Tern (v100,v103,(Tern (v3,v102,(Tern (v2,v102,v100)))))
Tern (v102,v100,(Tern (v2,v3,v102))) = Tern (v3,v102,(Tern (v2,v102,v100))) by A739;
hence Tern (v100,(Tern (v2,v3,v102)),(Tern (v102,v100,v103))) = Tern (v100,v103,(Tern (v3,v102,(Tern (v2,v102,v100))))) by A670; :: thesis: verum
end;
A918: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,v3))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v1,v3,v0)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,v3))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v1,v3,v0)))))
Tern (v0,v4,v3) = Tern (v3,v0,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,v3))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v1,v3,v0))))) by A915; :: thesis: verum
end;
A920: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v1,v3,v0)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v1,v3,v0)))))
Tern (v0,v4,v3) = Tern (v0,v3,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v1,v3,v0))))) by A918; :: thesis: verum
end;
A922: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v3)))))
Tern (v1,v3,v0) = Tern (v0,v1,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,v4))) = Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v3))))) by A920; :: thesis: verum
end;
A925: for v3, v2, v100, v1 being Element of (BA2TBAA B) holds Tern (v1,v100,v2) = Tern (v100,(Tern (v1,v100,v2)),(Tern (v1,v2,v3)))
proof
let v3, v2, v100, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v100,v2) = Tern (v100,(Tern (v1,v100,v2)),(Tern (v1,v2,v3)))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v1,v100,v2))) = Tern (v1,v100,v2) by A807;
hence Tern (v1,v100,v2) = Tern (v100,(Tern (v1,v100,v2)),(Tern (v1,v2,v3))) by A4; :: thesis: verum
end;
A931: for v100, v103, v2, v3, v1, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,(Tern (v1,v2,(Tern (v101,v1,v3)))),v103)),(Tern (v101,v100,(Tern (v1,v2,(Tern (v101,v1,v3))))))) = Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v100,v1)))
proof
let v100, v103, v2, v3, v1, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,(Tern (v1,v2,(Tern (v101,v1,v3)))),v103)),(Tern (v101,v100,(Tern (v1,v2,(Tern (v101,v1,v3))))))) = Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v100,v1)))
Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v100,v1))) = Tern (v101,v100,(Tern (v1,v2,(Tern (v101,v1,v3))))) by A149;
hence Tern (v100,(Tern (v101,(Tern (v1,v2,(Tern (v101,v1,v3)))),v103)),(Tern (v101,v100,(Tern (v1,v2,(Tern (v101,v1,v3))))))) = Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v100,v1))) by A807; :: thesis: verum
end;
A934: for v0, v5, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v5,(Tern (v2,v3,(Tern (v1,v2,v4)))))),(Tern (v1,v0,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2)))
proof
let v0, v5, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v5,(Tern (v2,v3,(Tern (v1,v2,v4)))))),(Tern (v1,v0,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2)))
Tern (v1,(Tern (v2,v3,(Tern (v1,v2,v4)))),v5) = Tern (v1,v5,(Tern (v2,v3,(Tern (v1,v2,v4))))) by A4;
hence Tern (v0,(Tern (v1,v5,(Tern (v2,v3,(Tern (v1,v2,v4)))))),(Tern (v1,v0,(Tern (v2,v3,(Tern (v1,v2,v4))))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2))) by A931; :: thesis: verum
end;
A937: for v0, v2, v4, v5, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),v1))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3)))
proof
let v0, v2, v4, v5, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),v1))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3)))
Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),v1) = Tern (v1,v0,(Tern (v3,v4,(Tern (v1,v3,v5))))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),v1))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3))) by A934; :: thesis: verum
end;
A939: for v0, v2, v4, v5, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,v1,(Tern (v3,v4,(Tern (v1,v3,v5))))))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3)))
proof
let v0, v2, v4, v5, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,v1,(Tern (v3,v4,(Tern (v1,v3,v5))))))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3)))
Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),v1) = Tern (v0,v1,(Tern (v3,v4,(Tern (v1,v3,v5))))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,v1,(Tern (v3,v4,(Tern (v1,v3,v5))))))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3))) by A937; :: thesis: verum
end;
A941: for v2, v0, v4, v5, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5))))))))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3)))
proof
let v2, v0, v4, v5, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5))))))))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3)))
Tern (v0,(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5)))))),(Tern (v0,v1,(Tern (v3,v4,(Tern (v1,v3,v5))))))) = Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5))))))))) by A492;
hence Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v1,v3,v5)))),(Tern (v1,v2,(Tern (v3,v4,(Tern (v1,v3,v5))))))))) = Tern (v1,(Tern (v3,v4,v5)),(Tern (v1,v0,v3))) by A939; :: thesis: verum
end;
A944: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2)))
proof
now :: thesis: for v5, v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2)))
let v5, v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2)))
Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v2,v4)))),(Tern (v1,v5,(Tern (v2,v3,(Tern (v1,v2,v4))))))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) by A836;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2))) by A941; :: thesis: verum
end;
hence for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v0,v2))) ; :: thesis: verum
end;
A946: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v1)))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v1)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v1))) by A944; :: thesis: verum
end;
A948: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v1,v2)))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) by A946; :: thesis: verum
end;
A953: for v102, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v102,v2,v3)),v102) = Tern (v102,v2,v3)
proof
let v102, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v102,v2,v3)),v102) = Tern (v102,v2,v3)
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v2,v3))) = Tern (v102,v2,v3) by A822;
hence Tern ((Tern (v1,v2,v3)),(Tern (v102,v2,v3)),v102) = Tern (v102,v2,v3) by A3; :: thesis: verum
end;
A956: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v1)),v3) = Tern (v3,v1,v2)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v1)),v3) = Tern (v3,v1,v2)
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v1)),v3) = Tern (v3,v1,v2) by A953; :: thesis: verum
end;
A958: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v3) = Tern (v3,v1,v2)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v3) = Tern (v3,v1,v2)
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v3) = Tern (v3,v1,v2) by A956; :: thesis: verum
end;
A960: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern (v3,v1,v2)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern (v3,v1,v2)
Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern (v3,v1,v2) by A958; :: thesis: verum
end;
A963: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v0))) = Tern (v3,v0,v2)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v0))) = Tern (v3,v0,v2)
Tern (v0,v2,v3) = Tern (v3,v0,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v0))) = Tern (v3,v0,v2) by A960; :: thesis: verum
end;
A965: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v0))) = Tern (v2,v3,v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v0))) = Tern (v2,v3,v0)
Tern (v3,v0,v2) = Tern (v2,v3,v0) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v0))) = Tern (v2,v3,v0) by A963; :: thesis: verum
end;
A968: for v103, v100, v102, v104, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v104,v102)),(Tern (v100,v102,(Tern (v100,v103,v104))))) = Tern (v100,v103,(Tern (v100,v104,v102)))
proof
let v103, v100, v102, v104, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v104,v102)),(Tern (v100,v102,(Tern (v100,v103,v104))))) = Tern (v100,v103,(Tern (v100,v104,v102)))
Tern (v100,(Tern (v1,v104,v102)),(Tern (v100,v104,v102))) = Tern (v100,v104,v102) by A822;
hence Tern (v100,(Tern (v1,v104,v102)),(Tern (v100,v102,(Tern (v100,v103,v104))))) = Tern (v100,v103,(Tern (v100,v104,v102))) by A139; :: thesis: verum
end;
A971: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,v4))))) = Tern (v0,v4,(Tern (v0,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,v4))))) = Tern (v0,v4,(Tern (v0,v2,v3)))
Tern (v0,v4,v2) = Tern (v0,v2,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,v4))))) = Tern (v0,v4,(Tern (v0,v2,v3))) by A968; :: thesis: verum
end;
A974: for v100, v1, v3, v2, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v101,(Tern (v101,v2,v3)))),(Tern (v100,(Tern (v1,v101,v2)),(Tern (v101,v2,v3))))) = Tern (v100,(Tern (v1,v101,v2)),(Tern (v101,v2,v3)))
proof
let v100, v1, v3, v2, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v101,(Tern (v101,v2,v3)))),(Tern (v100,(Tern (v1,v101,v2)),(Tern (v101,v2,v3))))) = Tern (v100,(Tern (v1,v101,v2)),(Tern (v101,v2,v3)))
Tern (v101,(Tern (v1,v101,v2)),(Tern (v101,v2,v3))) = Tern (v1,v101,(Tern (v101,v2,v3))) by A517;
hence Tern (v100,(Tern (v1,v101,(Tern (v101,v2,v3)))),(Tern (v100,(Tern (v1,v101,v2)),(Tern (v101,v2,v3))))) = Tern (v100,(Tern (v1,v101,v2)),(Tern (v101,v2,v3))) by A822; :: thesis: verum
end;
A978: for v102, v100, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v102,(Tern (v102,v2,v3))))) = Tern (v100,v102,(Tern (v1,v2,v3)))
proof
let v102, v100, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v102,(Tern (v102,v2,v3))))) = Tern (v100,v102,(Tern (v1,v2,v3)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v2,v3))) = Tern (v102,v2,v3) by A822;
hence Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v102,(Tern (v102,v2,v3))))) = Tern (v100,v102,(Tern (v1,v2,v3))) by A594; :: thesis: verum
end;
A981: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v3,v4,v2))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v3,v4,v2))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v3,v4,v2))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A978; :: thesis: verum
end;
A983: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v2,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v2,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v2,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A981; :: thesis: verum
end;
A986: for v103, v102, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v102,v2,v3)),(Tern (v102,(Tern (v1,v2,v3)),v103))) = Tern ((Tern (v1,v2,v3)),v103,(Tern (v102,v2,v3)))
proof
let v103, v102, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v102,v2,v3)),(Tern (v102,(Tern (v1,v2,v3)),v103))) = Tern ((Tern (v1,v2,v3)),v103,(Tern (v102,v2,v3)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v2,v3))) = Tern (v102,v2,v3) by A822;
hence Tern ((Tern (v1,v2,v3)),(Tern (v102,v2,v3)),(Tern (v102,(Tern (v1,v2,v3)),v103))) = Tern ((Tern (v1,v2,v3)),v103,(Tern (v102,v2,v3))) by A670; :: thesis: verum
end;
A989: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v1)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v1)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2)))
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v1)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2))) by A986; :: thesis: verum
end;
A991: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2)))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2))) by A989; :: thesis: verum
end;
A993: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2)))
Tern (v3,(Tern (v0,v1,v2)),v4) = Tern (v3,v4,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v3,v1,v2))) by A991; :: thesis: verum
end;
A995: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v2,v3,v1)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v2,v3,v1)))
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v2,v3,v1))) by A993; :: thesis: verum
end;
A997: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v1,v2,v3)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v1,v2,v3)))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v1,v2,v3))) by A995; :: thesis: verum
end;
A999: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))
Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v4,(Tern (v1,v2,v3))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) by A997; :: thesis: verum
end;
A1002: for v100, v101, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v2,v3)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100)
proof
let v100, v101, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v2,v3)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100)
Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v2,v3))) = Tern (v101,v2,v3) by A822;
hence Tern (v100,(Tern (v101,v2,v3)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100) by A729; :: thesis: verum
end;
A1005: for v0, v1, v2, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v3,v4,v2)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v0, v1, v2, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v3,v4,v2)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v3,v4,v2)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1002; :: thesis: verum
end;
A1007: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v2,v3,v4)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v2,v3,v4)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v2,v3,v4)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1005; :: thesis: verum
end;
A1009: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v1,(Tern (v2,v3,v4)),v0) = Tern (v0,v1,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1007; :: thesis: verum
end;
A1011: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) by A492;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1009; :: thesis: verum
end;
A1013: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v3,v4,v2)),v0)
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v3,v4,v2)),v0)
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v3,v4,v2)),v0) by A1011; :: thesis: verum
end;
A1015: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v2,v3,v4)),v0)
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v2,v3,v4)),v0)
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v2,v3,v4)),v0) by A1013; :: thesis: verum
end;
A1017: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v0,v1,(Tern (v2,v3,v4)))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v0,v1,(Tern (v2,v3,v4)))
Tern (v1,(Tern (v2,v3,v4)),v0) = Tern (v0,v1,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v0,v1,(Tern (v2,v3,v4))) by A1015; :: thesis: verum
end;
A1020: for v100, v2, v3, v102, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,v100)),(Tern (v101,v2,(Tern (v101,v102,v3))))) = Tern (v101,v102,v100)
proof
let v100, v2, v3, v102, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,v100)),(Tern (v101,v2,(Tern (v101,v102,v3))))) = Tern (v101,v102,v100)
Tern (v101,v102,(Tern (v101,v2,v3))) = Tern (v101,v2,(Tern (v101,v102,v3))) by A27;
hence Tern (v100,(Tern (v101,v102,v100)),(Tern (v101,v2,(Tern (v101,v102,v3))))) = Tern (v101,v102,v100) by A839; :: thesis: verum
end;
A1023: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v1,v2,v4))))) = Tern (v1,v2,v0)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v1,v2,v4))))) = Tern (v1,v2,v0)
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v1,v2,v4))))) = Tern (v1,v2,v0) by A1020; :: thesis: verum
end;
A1025: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v1,v2,v4))))) = Tern (v0,v1,v2)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v1,v2,v4))))) = Tern (v0,v1,v2)
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v1,v3,(Tern (v1,v2,v4))))) = Tern (v0,v1,v2) by A1023; :: thesis: verum
end;
A1028: for v100, v103, v102, v3, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v3,v102)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v3,v102)),v103))))) = Tern (v3,v102,(Tern (v100,v2,v102)))
proof
let v100, v103, v102, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v3,v102)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v3,v102)),v103))))) = Tern (v3,v102,(Tern (v100,v2,v102)))
Tern (v100,v102,(Tern (v2,v3,v102))) = Tern (v3,v102,(Tern (v100,v2,v102))) by A898;
hence Tern (v100,(Tern (v2,v3,v102)),(Tern (v100,v102,(Tern (v102,(Tern (v2,v3,v102)),v103))))) = Tern (v3,v102,(Tern (v100,v2,v102))) by A594; :: thesis: verum
end;
A1031: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v2,v3,(Tern (v0,v1,v3)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v2,v3,(Tern (v0,v1,v3)))
Tern (v3,(Tern (v1,v2,v3)),v4) = Tern (v3,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v2,v3,(Tern (v0,v1,v3))) by A1028; :: thesis: verum
end;
A1033: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v1,v3,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v3)))
proof
now :: thesis: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v3,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v3)))
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v3,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v3)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v3,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v0,v2,v3))) by A815;
hence Tern (v1,v3,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v3))) by A1031; :: thesis: verum
end;
hence for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v1,v3,(Tern (v0,v2,v3))) = Tern (v2,v3,(Tern (v0,v1,v3))) ; :: thesis: verum
end;
A1037: for v100, v101, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v101,(Tern (v1,v2,v3)),(Tern (v1,v2,v100))))) = Tern (v100,v101,(Tern (v1,v2,v3)))
proof
let v100, v101, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v101,(Tern (v1,v2,v3)),(Tern (v1,v2,v100))))) = Tern (v100,v101,(Tern (v1,v2,v3)))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v1,v2,v100))) = Tern (v1,v2,v100) by A729;
hence Tern (v100,v101,(Tern (v101,(Tern (v1,v2,v3)),(Tern (v1,v2,v100))))) = Tern (v100,v101,(Tern (v1,v2,v3))) by A608; :: thesis: verum
end;
A1040: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v3))))) = Tern (v0,v1,(Tern (v2,v3,v4)))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v3))))) = Tern (v0,v1,(Tern (v2,v3,v4)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,v1,(Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v2,v3))))) = Tern (v0,v1,(Tern (v2,v3,v4))) by A1037; :: thesis: verum
end;
A1043: for v100, v102, v5, v4, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v103,(Tern (v103,v4,v5)))),(Tern (v102,v103,v100))) = Tern (v102,v103,(Tern (v102,v100,(Tern (v103,v4,(Tern (v103,v100,v5)))))))
proof
let v100, v102, v5, v4, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v103,(Tern (v103,v4,v5)))),(Tern (v102,v103,v100))) = Tern (v102,v103,(Tern (v102,v100,(Tern (v103,v4,(Tern (v103,v100,v5)))))))
Tern (v102,v100,(Tern (v103,v100,(Tern (v102,v103,(Tern (v103,v4,v5))))))) = Tern (v102,v103,(Tern (v102,v100,(Tern (v103,v4,(Tern (v103,v100,v5))))))) by A186;
hence Tern (v100,(Tern (v102,v103,(Tern (v103,v4,v5)))),(Tern (v102,v103,v100))) = Tern (v102,v103,(Tern (v102,v100,(Tern (v103,v4,(Tern (v103,v100,v5))))))) by A708; :: thesis: verum
end;
A1046: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4)))))))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4)))))))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v1,v2))) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4))))))) by A1043; :: thesis: verum
end;
A1048: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,(Tern (v2,v3,v4))))))) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4)))))))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,(Tern (v2,v3,v4))))))) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4)))))))
Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v1,v2))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,(Tern (v2,v3,v4))))))) by A492;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,(Tern (v2,v3,v4))))))) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4))))))) by A1046; :: thesis: verum
end;
A1050: for v1, v3, v4, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4)))))))
proof
let v1, v3, v4, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4)))))))
Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v2,(Tern (v2,v3,v4))))))) = Tern (v0,v1,v2) by A616;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v2,v0,v4))))))) by A1048; :: thesis: verum
end;
A1052: for v1, v3, v2, v4, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v4,v2)))))))
proof
let v1, v3, v2, v4, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v4,v2)))))))
Tern (v0,v4,v2) = Tern (v2,v0,v4) by A3;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v4,v2))))))) by A1050; :: thesis: verum
end;
A1054: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
Tern (v0,v4,v2) = Tern (v0,v2,v4) by A4;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v2,v4))))))) by A1052; :: thesis: verum
end;
A1056: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1)))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1)))
Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1) = Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v2,v4))))) by A3;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1))) by A1054; :: thesis: verum
end;
A1058: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))))
Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) by A4;
hence Tern (v0,v1,v2) = Tern (v1,v2,(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))))) by A1056; :: thesis: verum
end;
A1063: for v101, v103, v102, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v102,v103)),v101,(Tern (v1,v102,(Tern (v102,v101,v103))))) = Tern (v102,(Tern (v1,v102,v103)),v101)
proof
let v101, v103, v102, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v102,v103)),v101,(Tern (v1,v102,(Tern (v102,v101,v103))))) = Tern (v102,(Tern (v1,v102,v103)),v101)
Tern (v102,(Tern (v1,v102,v103)),(Tern (v102,v101,v103))) = Tern (v1,v102,(Tern (v102,v101,v103))) by A504;
hence Tern ((Tern (v1,v102,v103)),v101,(Tern (v1,v102,(Tern (v102,v101,v103))))) = Tern (v102,(Tern (v1,v102,v103)),v101) by A697; :: thesis: verum
end;
A1066: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v0,v1,v2)),v3)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v0,v1,v2)),v3)
Tern (v1,v3,v2) = Tern (v1,v2,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v0,v1,v2)),v3) by A1063; :: thesis: verum
end;
A1068: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern (v1,(Tern (v0,v1,v2)),v3)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern (v1,(Tern (v0,v1,v2)),v3)
Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v1,v2,v3))))) by A3;
hence Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern (v1,(Tern (v0,v1,v2)),v3) by A1066; :: thesis: verum
end;
A1071: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) = Tern (v2,(Tern (v1,v2,v3)),v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) = Tern (v2,(Tern (v1,v2,v3)),v0)
Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v1,v2,v3))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) = Tern (v2,(Tern (v1,v2,v3)),v0) by A1068; :: thesis: verum
end;
A1073: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) = Tern (v2,v0,(Tern (v1,v2,v3)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) = Tern (v2,v0,(Tern (v1,v2,v3)))
Tern (v2,(Tern (v1,v2,v3)),v0) = Tern (v2,v0,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v2,v3,v0))))) = Tern (v2,v0,(Tern (v1,v2,v3))) by A1071; :: thesis: verum
end;
A1076: for v101, v100, v102, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,(Tern (v3,v4,v5))))))) = Tern (v100,(Tern (v3,v4,(Tern (v100,v3,v5)))),(Tern (v100,v101,v102)))
proof
let v101, v100, v102, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,(Tern (v3,v4,v5))))))) = Tern (v100,(Tern (v3,v4,(Tern (v100,v3,v5)))),(Tern (v100,v101,v102)))
Tern (v100,v101,(Tern (v100,v102,(Tern (v3,v4,(Tern (v100,v3,v5))))))) = Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,(Tern (v3,v4,v5))))))) by A189;
hence Tern (v100,v3,(Tern (v100,v101,(Tern (v100,v102,(Tern (v3,v4,v5))))))) = Tern (v100,(Tern (v3,v4,(Tern (v100,v3,v5)))),(Tern (v100,v101,v102))) by A55; :: thesis: verum
end;
A1082: for v100, v1, v4, v101, v103 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,(Tern (v1,v103,(Tern (v103,v101,v4)))),(Tern (v100,v103,v101))))) = Tern (v100,v103,v101)
proof
let v100, v1, v4, v101, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,(Tern (v1,v103,(Tern (v103,v101,v4)))),(Tern (v100,v103,v101))))) = Tern (v100,v103,v101)
Tern (v100,(Tern (v1,v103,(Tern (v103,v101,v4)))),(Tern (v100,v103,v101))) = Tern (v100,v103,v101) by A850;
hence Tern (v100,v101,(Tern (v100,(Tern (v1,v103,(Tern (v103,v101,v4)))),(Tern (v100,v103,v101))))) = Tern (v100,v103,v101) by A78; :: thesis: verum
end;
A1085: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v4,v3)))),(Tern (v0,v3,v1))))) = Tern (v0,v3,v1)
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v4,v3)))),(Tern (v0,v3,v1))))) = Tern (v0,v3,v1)
Tern (v1,v4,v3) = Tern (v3,v1,v4) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v4,v3)))),(Tern (v0,v3,v1))))) = Tern (v0,v3,v1) by A1082; :: thesis: verum
end;
A1087: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v3,v1))))) = Tern (v0,v3,v1)
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v3,v1))))) = Tern (v0,v3,v1)
Tern (v1,v4,v3) = Tern (v1,v3,v4) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v3,v1))))) = Tern (v0,v3,v1) by A1085; :: thesis: verum
end;
A1089: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))))) = Tern (v0,v3,v1)
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))))) = Tern (v0,v3,v1)
Tern (v0,v3,v1) = Tern (v0,v1,v3) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))))) = Tern (v0,v3,v1) by A1087; :: thesis: verum
end;
A1091: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))) = Tern (v0,v3,v1)
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))) = Tern (v0,v3,v1)
Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))))) = Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))) by A89;
hence Tern (v0,(Tern (v2,v3,(Tern (v1,v3,v4)))),(Tern (v0,v1,v3))) = Tern (v0,v3,v1) by A1089; :: thesis: verum
end;
A1094: for v0, v1, v4, v2, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v3,v2,v4)))),(Tern (v0,v3,v2))) = Tern (v0,v3,v2)
proof
let v0, v1, v4, v2, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v3,v2,v4)))),(Tern (v0,v3,v2))) = Tern (v0,v3,v2)
Tern (v0,v2,v3) = Tern (v0,v3,v2) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v3,v2,v4)))),(Tern (v0,v3,v2))) = Tern (v0,v3,v2) by A1091; :: thesis: verum
end;
A1097: for v103, v104, v2, v3, v101, v100 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v101,(Tern (v100,v101,v3)))),(Tern (v100,v103,v104))) = Tern (v100,v101,(Tern (v100,v103,(Tern (v100,v104,(Tern (v2,v101,v3)))))))
proof
let v103, v104, v2, v3, v101, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v101,(Tern (v100,v101,v3)))),(Tern (v100,v103,v104))) = Tern (v100,v101,(Tern (v100,v103,(Tern (v100,v104,(Tern (v2,v101,v3)))))))
Tern (v100,v101,(Tern (v2,v101,v3))) = Tern (v2,v101,(Tern (v100,v101,v3))) by A100;
hence Tern (v100,(Tern (v2,v101,(Tern (v100,v101,v3)))),(Tern (v100,v103,v104))) = Tern (v100,v101,(Tern (v100,v103,(Tern (v100,v104,(Tern (v2,v101,v3))))))) by A193; :: thesis: verum
end;
A1101: for v3, v2, v103, v101 being Element of (BA2TBAA B) holds Tern ((Tern (v3,v103,v2)),(Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2)))),(Tern (v101,v103,v2))) = Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2)))
proof
let v3, v2, v103, v101 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,v103,v2)),(Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2)))),(Tern (v101,v103,v2))) = Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2)))
Tern (v101,v103,(Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2))))) = Tern (v101,v103,v2) by A771;
hence Tern ((Tern (v3,v103,v2)),(Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2)))),(Tern (v101,v103,v2))) = Tern (v101,(Tern (v101,v103,v2)),(Tern (v3,v103,v2))) by A910; :: thesis: verum
end;
A1104: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v2,v3,v1)),(Tern (v0,v1,v2)))),(Tern (v3,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v2,v3,v1)),(Tern (v0,v1,v2)))),(Tern (v3,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v2,v3,v1)),(Tern (v0,v1,v2)))),(Tern (v3,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2))) by A1101; :: thesis: verum
end;
A1106: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v3,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v3,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v3,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2))) by A1104; :: thesis: verum
end;
A1108: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v2,v3,v1))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v2,v3,v1))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v2,v3,v1))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2))) by A1106; :: thesis: verum
end;
A1110: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v1,v2,v3))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v1,v2,v3))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v1,v2,v3))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2))) by A1108; :: thesis: verum
end;
A1112: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2)))),(Tern (v1,v2,v3))) = Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2))) by A1110; :: thesis: verum
end;
A1114: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v3,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) by A999;
hence Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v3,v1,v2)),(Tern (v0,v1,v2))) by A1112; :: thesis: verum
end;
A1117: for v3, v1, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v2,v0,v1)),(Tern (v3,v0,v1)))
proof
let v3, v1, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v2,v0,v1)),(Tern (v3,v0,v1)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v0,v1))) = Tern (v0,v1,v2) by A2;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v2,v0,v1)),(Tern (v3,v0,v1))) by A1114; :: thesis: verum
end;
A1119: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v1,v2,v0)),(Tern (v3,v0,v1)))
proof
let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v1,v2,v0)),(Tern (v3,v0,v1)))
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v1,v2,v0)),(Tern (v3,v0,v1))) by A1117; :: thesis: verum
end;
A1121: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v3,v0,v1)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v3,v0,v1)))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v1,v2)),(Tern (v3,v0,v1))) by A1119; :: thesis: verum
end;
A1126: for v4, v2, v100, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v100,v2)),(Tern (v102,v100,v2))) = Tern (v102,(Tern (v102,v100,v2)),(Tern (v100,(Tern (v102,v100,v2)),(Tern (v100,v2,v4)))))
proof
let v4, v2, v100, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v100,v2)),(Tern (v102,v100,v2))) = Tern (v102,(Tern (v102,v100,v2)),(Tern (v100,(Tern (v102,v100,v2)),(Tern (v100,v2,v4)))))
Tern (v102,(Tern (v102,v100,v2)),(Tern (v100,(Tern (v102,v100,v2)),(Tern (v100,v2,v4))))) = Tern (v102,v100,v2) by A1025;
hence Tern (v100,(Tern (v102,v100,v2)),(Tern (v102,v100,v2))) = Tern (v102,(Tern (v102,v100,v2)),(Tern (v100,(Tern (v102,v100,v2)),(Tern (v100,v2,v4))))) by A311; :: thesis: verum
end;
A1129: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v2,v1)),(Tern (v1,v0,v2))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v2,v1)),(Tern (v1,v0,v2))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,(Tern (v0,v2,v1)),(Tern (v1,v0,v2))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))))) by A1126; :: thesis: verum
end;
A1132: for v3, v1, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v2,v1)),(Tern (v2,v0,v1))) = Tern (v2,(Tern (v2,v0,v1)),(Tern (v0,(Tern (v2,v0,v1)),(Tern (v0,v1,v3)))))
proof
let v3, v1, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v2,v1)),(Tern (v2,v0,v1))) = Tern (v2,(Tern (v2,v0,v1)),(Tern (v0,(Tern (v2,v0,v1)),(Tern (v0,v1,v3)))))
Tern (v0,v1,v2) = Tern (v0,v2,v1) by A4;
hence Tern (v0,(Tern (v0,v2,v1)),(Tern (v2,v0,v1))) = Tern (v2,(Tern (v2,v0,v1)),(Tern (v0,(Tern (v2,v0,v1)),(Tern (v0,v1,v3))))) by A1129; :: thesis: verum
end;
A1135: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v1))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v1))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v1))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))))) by A1132; :: thesis: verum
end;
A1137: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))))) by A1135; :: thesis: verum
end;
A1139: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A34;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v1,v0,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))))) by A1137; :: thesis: verum
end;
A1141: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))))) by A1139; :: thesis: verum
end;
A1143: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v1,v0,v2)),(Tern (v0,v2,v3))))) by A1141; :: thesis: verum
end;
A1145: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v2,v1)),(Tern (v0,v2,v3)))))
proof
let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v2,v1)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v2,v1)),(Tern (v0,v2,v3))))) by A1143; :: thesis: verum
end;
A1147: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v3)))))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v3)))))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))))) by A1145; :: thesis: verum
end;
A1149: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v2)))))))
proof
let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v2)))))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v2))))) by A193;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v2))))))) by A1147; :: thesis: verum
end;
A1151: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v2,v3)))))))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v2,v3)))))))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v2,v3))))))) by A1149; :: thesis: verum
end;
A1153: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3)))))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3)))))
Tern (v0,v2,(Tern (v0,v2,v3))) = Tern (v0,v2,v3) by A74;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v0,v2,v3))))) by A1151; :: thesis: verum
end;
A1158: for v101, v100, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v100,(Tern (v1,v2,v3)))),(Tern (v101,v100,(Tern (v101,v2,v3))))) = Tern (v101,v100,(Tern (v1,v2,v3)))
proof
let v101, v100, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v100,(Tern (v1,v2,v3)))),(Tern (v101,v100,(Tern (v101,v2,v3))))) = Tern (v101,v100,(Tern (v1,v2,v3)))
Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v2,v3))) = Tern (v101,v2,v3) by A822;
hence Tern (v100,(Tern (v101,v100,(Tern (v1,v2,v3)))),(Tern (v101,v100,(Tern (v101,v2,v3))))) = Tern (v101,v100,(Tern (v1,v2,v3))) by A1153; :: thesis: verum
end;
A1161: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,(Tern (v2,v3,v4)),v1)),(Tern (v1,v0,(Tern (v1,v3,v4))))) = Tern (v1,v0,(Tern (v2,v3,v4)))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,(Tern (v2,v3,v4)),v1)),(Tern (v1,v0,(Tern (v1,v3,v4))))) = Tern (v1,v0,(Tern (v2,v3,v4)))
Tern (v0,(Tern (v2,v3,v4)),v1) = Tern (v1,v0,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,(Tern (v0,(Tern (v2,v3,v4)),v1)),(Tern (v1,v0,(Tern (v1,v3,v4))))) = Tern (v1,v0,(Tern (v2,v3,v4))) by A1158; :: thesis: verum
end;
A1164: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v4,v0,(Tern (v4,v2,v3))))) = Tern (v4,v0,(Tern (v1,v2,v3)))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v4,v0,(Tern (v4,v2,v3))))) = Tern (v4,v0,(Tern (v1,v2,v3)))
Tern (v0,(Tern (v1,v2,v3)),v4) = Tern (v0,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v4,v0,(Tern (v4,v2,v3))))) = Tern (v4,v0,(Tern (v1,v2,v3))) by A1161; :: thesis: verum
end;
A1167: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v1,v3,v4)),v1))) = Tern (v1,v0,(Tern (v2,v3,v4)))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v1,v3,v4)),v1))) = Tern (v1,v0,(Tern (v2,v3,v4)))
Tern (v0,(Tern (v1,v3,v4)),v1) = Tern (v1,v0,(Tern (v1,v3,v4))) by A3;
hence Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v1,v3,v4)),v1))) = Tern (v1,v0,(Tern (v2,v3,v4))) by A1164; :: thesis: verum
end;
A1169: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,v1,(Tern (v1,v3,v4))))) = Tern (v1,v0,(Tern (v2,v3,v4)))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,v1,(Tern (v1,v3,v4))))) = Tern (v1,v0,(Tern (v2,v3,v4)))
Tern (v0,(Tern (v1,v3,v4)),v1) = Tern (v0,v1,(Tern (v1,v3,v4))) by A4;
hence Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,v1,(Tern (v1,v3,v4))))) = Tern (v1,v0,(Tern (v2,v3,v4))) by A1167; :: thesis: verum
end;
A1171: for v2, v0, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v2,v3,v4))))))) = Tern (v1,v0,(Tern (v2,v3,v4)))
proof
let v2, v0, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v2,v3,v4))))))) = Tern (v1,v0,(Tern (v2,v3,v4)))
Tern (v0,(Tern (v0,v1,(Tern (v2,v3,v4)))),(Tern (v0,v1,(Tern (v1,v3,v4))))) = Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v2,v3,v4))))))) by A193;
hence Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v2,v3,v4))))))) = Tern (v1,v0,(Tern (v2,v3,v4))) by A1169; :: thesis: verum
end;
A1174: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v1,v0,(Tern (v4,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v1,v0,(Tern (v4,v2,v3)))
Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))))) = Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) by A74;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v1,v0,(Tern (v4,v2,v3))) by A1171; :: thesis: verum
end;
A1176: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v0,(Tern (v4,v2,v3)),v1)
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v0,(Tern (v4,v2,v3)),v1)
Tern (v0,(Tern (v4,v2,v3)),v1) = Tern (v1,v0,(Tern (v4,v2,v3))) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v0,(Tern (v4,v2,v3)),v1) by A1174; :: thesis: verum
end;
A1178: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v0,v1,(Tern (v4,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v0,v1,(Tern (v4,v2,v3)))
Tern (v0,(Tern (v4,v2,v3)),v1) = Tern (v0,v1,(Tern (v4,v2,v3))) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,v3))))) = Tern (v0,v1,(Tern (v4,v2,v3))) by A1176; :: thesis: verum
end;
A1181: for v3, v4, v100, v101, v102 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,v3,(Tern (v102,v4,(Tern (v102,v101,v100))))))) = Tern (v102,v100,v101)
proof
let v3, v4, v100, v101, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,v3,(Tern (v102,v4,(Tern (v102,v101,v100))))))) = Tern (v102,v100,v101)
Tern (v102,v101,(Tern (v102,v100,(Tern (v102,v3,v4))))) = Tern (v102,v3,(Tern (v102,v4,(Tern (v102,v101,v100))))) by A198;
hence Tern (v100,v101,(Tern (v102,v3,(Tern (v102,v4,(Tern (v102,v101,v100))))))) = Tern (v102,v100,v101) by A693; :: thesis: verum
end;
A1184: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v2,v1))))))) = Tern (v2,v0,v1)
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v2,v1))))))) = Tern (v2,v0,v1)
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v2,v1))))))) = Tern (v2,v0,v1) by A1181; :: thesis: verum
end;
A1186: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,v1)
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,v1)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,v1) by A1184; :: thesis: verum
end;
A1188: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v1,v2,v0)
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v1,v2,v0)
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v1,v2,v0) by A1186; :: thesis: verum
end;
A1190: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2)
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2)
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2) by A1188; :: thesis: verum
end;
A1193: for v103, v104, v100, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,(Tern (v100,v2,v4)),(Tern ((Tern (v100,v2,v4)),v103,(Tern ((Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,v2,v4)),v104))))))) = Tern (v100,v2,v4)
proof
let v103, v104, v100, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,(Tern (v100,v2,v4)),(Tern ((Tern (v100,v2,v4)),v103,(Tern ((Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,v2,v4)),v104))))))) = Tern (v100,v2,v4)
Tern (v100,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,v2,v4))) = Tern (v100,v2,v4) by A869;
hence Tern (v100,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,(Tern (v100,v2,v4)),(Tern ((Tern (v100,v2,v4)),v103,(Tern ((Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v100,v2,v4)),v104))))))) = Tern (v100,v2,v4) by A632; :: thesis: verum
end;
A1196: for v5, v0, v6, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v2,v4)
proof
let v5, v0, v6, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v2,v4)
Tern ((Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4)),v6) = Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v2,v4) by A1193; :: thesis: verum
end;
A1198: for v5, v0, v6, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))))))) = Tern (v0,v2,v4)
proof
let v5, v0, v6, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))))))) = Tern (v0,v2,v4)
Tern (v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))) = Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))))))) = Tern (v0,v2,v4) by A1196; :: thesis: verum
end;
A1200: for v5, v0, v6, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v2,v4)
proof
let v5, v0, v6, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v2,v4)
Tern (v5,(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))) = Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v2,v4) by A1198; :: thesis: verum
end;
A1203: for v100, v3, v4, v101, v102 being Element of (BA2TBAA B) holds Tern (v102,v100,v101) = Tern (v100,(Tern (v101,v3,(Tern (v102,v101,v4)))),(Tern (v102,v100,v101)))
proof
let v100, v3, v4, v101, v102 be Element of (BA2TBAA B); :: thesis: Tern (v102,v100,v101) = Tern (v100,(Tern (v101,v3,(Tern (v102,v101,v4)))),(Tern (v102,v100,v101)))
Tern (v100,v101,(Tern (v102,v100,(Tern (v101,v3,(Tern (v102,v101,v4))))))) = Tern (v102,v100,v101) by A1058;
hence Tern (v102,v100,v101) = Tern (v100,(Tern (v101,v3,(Tern (v102,v101,v4)))),(Tern (v102,v100,v101))) by A670; :: thesis: verum
end;
A1209: for v103, v3, v4, v2, v102, v101 being Element of (BA2TBAA B) holds Tern ((Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2)))))),(Tern (v101,v102,v103)),(Tern (v101,v102,(Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2))))))))) = Tern (v101,v102,v2)
proof
let v103, v3, v4, v2, v102, v101 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2)))))),(Tern (v101,v102,v103)),(Tern (v101,v102,(Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2))))))))) = Tern (v101,v102,v2)
Tern (v101,v102,(Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2))))))) = Tern (v101,v102,v2) by A1190;
hence Tern ((Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2)))))),(Tern (v101,v102,v103)),(Tern (v101,v102,(Tern (v2,v3,(Tern (v2,v4,(Tern (v101,v102,v2))))))))) = Tern (v101,v102,v2) by A729; :: thesis: verum
end;
A1212: for v5, v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v0))))))))) = Tern (v3,v4,v0)
proof
let v5, v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v0))))))))) = Tern (v3,v4,v0)
Tern (v3,v4,v0) = Tern (v0,v3,v4) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v0))))))))) = Tern (v3,v4,v0) by A1209; :: thesis: verum
end;
A1214: for v5, v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))))) = Tern (v3,v4,v0)
proof
let v5, v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))))) = Tern (v3,v4,v0)
Tern (v3,v4,v0) = Tern (v0,v3,v4) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))))) = Tern (v3,v4,v0) by A1212; :: thesis: verum
end;
A1216: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))) = Tern (v3,v4,v0)
proof
now :: thesis: for v5, v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))) = Tern (v3,v4,v0)
let v5, v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))) = Tern (v3,v4,v0)
Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4)))))),(Tern (v3,v4,v5)),(Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))) by A729;
hence Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))) = Tern (v3,v4,v0) by A1214; :: thesis: verum
end;
hence for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v3,v4))))))) = Tern (v3,v4,v0) ; :: thesis: verum
end;
A1219: for v3, v4, v1, v0, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v2,v0,v1))))))) = Tern (v2,v0,v1)
proof
let v3, v4, v1, v0, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v2,v0,v1))))))) = Tern (v2,v0,v1)
Tern (v0,v1,v2) = Tern (v2,v0,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v4,(Tern (v2,v0,v1))))))) = Tern (v2,v0,v1) by A1216; :: thesis: verum
end;
A1222: for v101, v4, v102, v100 being Element of (BA2TBAA B) holds Tern (v101,v100,(Tern (v100,v101,(Tern (v100,v102,v4))))) = Tern (v100,(Tern (v101,v100,v4)),(Tern (v100,v101,v102)))
proof
let v101, v4, v102, v100 be Element of (BA2TBAA B); :: thesis: Tern (v101,v100,(Tern (v100,v101,(Tern (v100,v102,v4))))) = Tern (v100,(Tern (v101,v100,v4)),(Tern (v100,v101,v102)))
Tern (v100,v101,(Tern (v100,v102,(Tern (v101,v100,v4))))) = Tern (v101,v100,(Tern (v100,v101,(Tern (v100,v102,v4))))) by A210;
hence Tern (v101,v100,(Tern (v100,v101,(Tern (v100,v102,v4))))) = Tern (v100,(Tern (v101,v100,v4)),(Tern (v100,v101,v102))) by A55; :: thesis: verum
end;
A1225: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),v1))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),v1))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2)))
Tern (v0,(Tern (v1,v2,v3)),v1) = Tern (v1,v0,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),v1))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2))) by A1222; :: thesis: verum
end;
A1227: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2)))
Tern (v0,(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,v1,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2))) by A1225; :: thesis: verum
end;
A1229: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2)))
Tern (v0,v1,(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v0,v1,(Tern (v1,v2,v3))) by A74;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v1,v0,v2))) by A1227; :: thesis: verum
end;
A1231: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v0,v2,v1)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v0,v2,v1)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v0,v2,v1))) by A1229; :: thesis: verum
end;
A1233: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A1231; :: thesis: verum
end;
A1238: for v104, v3, v103, v102 being Element of (BA2TBAA B) holds Tern (v104,(Tern (v102,v103,v3)),(Tern (v102,v103,(Tern ((Tern (v102,v103,v3)),v103,v104))))) = Tern ((Tern (v102,v103,v3)),v103,(Tern (v102,v103,v104)))
proof
let v104, v3, v103, v102 be Element of (BA2TBAA B); :: thesis: Tern (v104,(Tern (v102,v103,v3)),(Tern (v102,v103,(Tern ((Tern (v102,v103,v3)),v103,v104))))) = Tern ((Tern (v102,v103,v3)),v103,(Tern (v102,v103,v104)))
Tern (v104,(Tern (v102,v103,v3)),(Tern (v102,v103,v104))) = Tern (v102,v103,v104) by A729;
hence Tern (v104,(Tern (v102,v103,v3)),(Tern (v102,v103,(Tern ((Tern (v102,v103,v3)),v103,v104))))) = Tern ((Tern (v102,v103,v3)),v103,(Tern (v102,v103,v104))) by A236; :: thesis: verum
end;
A1241: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v2))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v2))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
Tern ((Tern (v1,v2,v3)),v2,v0) = Tern (v0,(Tern (v1,v2,v3)),v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v2))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0))) by A1238; :: thesis: verum
end;
A1243: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
Tern (v0,(Tern (v1,v2,v3)),v2) = Tern (v0,v2,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0))) by A1241; :: thesis: verum
end;
A1245: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
Tern (v1,v2,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v2,(Tern (v1,v2,v3))) by A311;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0))) by A1243; :: thesis: verum
end;
A1247: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v0,v2,(Tern (v1,v2,v3))) by A63;
hence Tern (v0,v2,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v2,(Tern (v1,v2,v0))) by A1245; :: thesis: verum
end;
A1250: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,v3))) = Tern ((Tern (v2,v1,v3)),v1,(Tern (v0,v2,v1)))
proof
let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,v3))) = Tern ((Tern (v2,v1,v3)),v1,(Tern (v0,v2,v1)))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v1,v3))) = Tern ((Tern (v2,v1,v3)),v1,(Tern (v0,v2,v1))) by A1247; :: thesis: verum
end;
A1252: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v1,v3)))
proof
let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v1,v3)))
Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v1,v3))) = Tern ((Tern (v2,v1,v3)),v1,(Tern (v0,v2,v1))) by A3;
hence Tern (v0,v1,(Tern (v2,v1,v3))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v1,v3))) by A1250; :: thesis: verum
end;
A1257: for v104, v103, v102, v1 being Element of (BA2TBAA B) holds Tern (v104,(Tern (v1,v102,v103)),(Tern (v102,v103,(Tern ((Tern (v1,v102,v103)),v103,v104))))) = Tern ((Tern (v1,v102,v103)),v103,(Tern (v102,v103,v104)))
proof
let v104, v103, v102, v1 be Element of (BA2TBAA B); :: thesis: Tern (v104,(Tern (v1,v102,v103)),(Tern (v102,v103,(Tern ((Tern (v1,v102,v103)),v103,v104))))) = Tern ((Tern (v1,v102,v103)),v103,(Tern (v102,v103,v104)))
Tern (v104,(Tern (v1,v102,v103)),(Tern (v102,v103,v104))) = Tern (v102,v103,v104) by A965;
hence Tern (v104,(Tern (v1,v102,v103)),(Tern (v102,v103,(Tern ((Tern (v1,v102,v103)),v103,v104))))) = Tern ((Tern (v1,v102,v103)),v103,(Tern (v102,v103,v104))) by A236; :: thesis: verum
end;
A1260: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,(Tern (v1,v2,v3)),v3))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,(Tern (v1,v2,v3)),v3))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0)))
Tern ((Tern (v1,v2,v3)),v3,v0) = Tern (v0,(Tern (v1,v2,v3)),v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,(Tern (v1,v2,v3)),v3))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0))) by A1257; :: thesis: verum
end;
A1262: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0)))
Tern (v0,(Tern (v1,v2,v3)),v3) = Tern (v0,v3,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0))) by A1260; :: thesis: verum
end;
A1264: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,v3,(Tern (v1,v2,v3))) by A753;
hence Tern (v0,v3,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v2,v3,v0))) by A1262; :: thesis: verum
end;
A1267: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v3,v1)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v3,v1)))
Tern (v3,v1,v0) = Tern (v0,v3,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v3,v1))) by A1264; :: thesis: verum
end;
A1269: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v1,(Tern (v0,v3,v1)),(Tern (v2,v3,v1)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v1,(Tern (v0,v3,v1)),(Tern (v2,v3,v1)))
Tern (v1,(Tern (v0,v3,v1)),(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v3,v1))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v1,(Tern (v0,v3,v1)),(Tern (v2,v3,v1))) by A1267; :: thesis: verum
end;
A1274: for v103, v101, v1, v3, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v102,v3,v1)),(Tern (v101,v102,(Tern (v102,v3,v1)))),(Tern (v102,v1,(Tern (v103,v102,v3))))) = Tern (v101,(Tern (v102,v3,v1)),(Tern (v103,v102,(Tern (v102,v3,v1)))))
proof
let v103, v101, v1, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v102,v3,v1)),(Tern (v101,v102,(Tern (v102,v3,v1)))),(Tern (v102,v1,(Tern (v103,v102,v3))))) = Tern (v101,(Tern (v102,v3,v1)),(Tern (v103,v102,(Tern (v102,v3,v1)))))
Tern (v102,v1,(Tern (v103,v102,v3))) = Tern (v103,v102,(Tern (v102,v3,v1))) by A134;
hence Tern ((Tern (v102,v3,v1)),(Tern (v101,v102,(Tern (v102,v3,v1)))),(Tern (v102,v1,(Tern (v103,v102,v3))))) = Tern (v101,(Tern (v102,v3,v1)),(Tern (v103,v102,(Tern (v102,v3,v1))))) by A1269; :: thesis: verum
end;
A1277: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v3)),(Tern (v0,v2,(Tern (v4,v0,v1))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v3)),(Tern (v0,v2,(Tern (v4,v0,v1))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v0,v1,v2)),v3) = Tern (v3,v0,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v3)),(Tern (v0,v2,(Tern (v4,v0,v1))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2))))) by A1274; :: thesis: verum
end;
A1279: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v4,v0,v1))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v4,v0,v1))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v0,v1,v2)),v3) = Tern (v0,v3,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v4,v0,v1))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2))))) by A1277; :: thesis: verum
end;
A1281: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v1,v4,v0))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v1,v4,v0))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
Tern (v4,v0,v1) = Tern (v1,v4,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v1,v4,v0))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2))))) by A1279; :: thesis: verum
end;
A1283: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2)))))
Tern (v1,v4,v0) = Tern (v0,v1,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v4,v0,(Tern (v0,v1,v2))))) by A1281; :: thesis: verum
end;
A1285: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v4)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v4)))
Tern (v0,(Tern (v0,v1,v2)),v4) = Tern (v4,v0,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,(Tern (v0,v1,v2)),v4))) by A1283; :: thesis: verum
end;
A1287: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v0,v1,v2)),v4) = Tern (v0,v4,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,(Tern (v0,v1,v2)))),(Tern (v0,v2,(Tern (v0,v1,v4))))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))) by A1285; :: thesis: verum
end;
A1290: for v103, v104, v100, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,(Tern (v100,v4,v2)),(Tern ((Tern (v100,v4,v2)),v103,(Tern ((Tern (v1,v2,v3)),(Tern (v100,v4,v2)),v104))))))) = Tern (v100,v4,(Tern (v1,v2,(Tern (v100,v2,v3)))))
proof
let v103, v104, v100, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,(Tern (v100,v4,v2)),(Tern ((Tern (v100,v4,v2)),v103,(Tern ((Tern (v1,v2,v3)),(Tern (v100,v4,v2)),v104))))))) = Tern (v100,v4,(Tern (v1,v2,(Tern (v100,v2,v3)))))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v4,v2))) = Tern (v100,v4,(Tern (v1,v2,(Tern (v100,v2,v3))))) by A239;
hence Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,(Tern (v100,v4,v2)),(Tern ((Tern (v100,v4,v2)),v103,(Tern ((Tern (v1,v2,v3)),(Tern (v100,v4,v2)),v104))))))) = Tern (v100,v4,(Tern (v1,v2,(Tern (v100,v2,v3))))) by A632; :: thesis: verum
end;
A1293: for v5, v6, v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v4,v2)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v4,v2)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v5, v6, v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v4,v2)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v4,v2)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern (v0,v4,v2) = Tern (v0,v2,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v4,v2)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v4,v2)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A1290; :: thesis: verum
end;
A1295: for v5, v6, v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v4,v2)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v5, v6, v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v4,v2)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern (v0,v4,v2) = Tern (v0,v2,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v4,v2)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A1293; :: thesis: verum
end;
A1297: for v5, v6, v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v2,v4)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v5, v6, v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v2,v4)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern (v0,v4,v2) = Tern (v0,v2,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern ((Tern (v1,v2,v3)),(Tern (v0,v2,v4)),v6))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A1295; :: thesis: verum
end;
A1299: for v5, v0, v4, v6, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v5, v0, v4, v6, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern ((Tern (v1,v2,v3)),(Tern (v0,v2,v4)),v6) = Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A1297; :: thesis: verum
end;
A1301: for v5, v0, v4, v6, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v5, v0, v4, v6, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern (v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))) = Tern ((Tern (v0,v2,v4)),v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A1299; :: thesis: verum
end;
A1303: for v5, v0, v4, v6, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
proof
let v5, v0, v4, v6, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3)))))
Tern (v5,(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4)))),(Tern (v0,v2,v4))) = Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,v3)),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,v3))))) by A1301; :: thesis: verum
end;
A1305: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,(Tern (v2,v3,v4))))))) = Tern (v0,v2,v4)
proof
now :: thesis: for v5, v0, v6, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,(Tern (v2,v3,v4))))))) = Tern (v0,v2,v4)
let v5, v0, v6, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,(Tern (v2,v3,v4))))))) = Tern (v0,v2,v4)
Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v0,v2,v4)),(Tern (v5,(Tern (v0,v2,v4)),(Tern (v6,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v2,v4))))))))) = Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,(Tern (v2,v3,v4))))))) by A1303;
hence Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,(Tern (v2,v3,v4))))))) = Tern (v0,v2,v4) by A1200; :: thesis: verum
end;
hence for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v4,(Tern (v1,v2,(Tern (v0,v2,(Tern (v2,v3,v4))))))) = Tern (v0,v2,v4) ; :: thesis: verum
end;
A1309: for v3, v103, v104, v2, v102, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v102,v2)),(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v104,(Tern (v1,v102,v2))))))) = Tern (v102,(Tern (v1,v102,v2)),(Tern (v1,v2,v3)))
proof
let v3, v103, v104, v2, v102, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v102,v2)),(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v104,(Tern (v1,v102,v2))))))) = Tern (v102,(Tern (v1,v102,v2)),(Tern (v1,v2,v3)))
Tern (v102,(Tern (v1,v102,v2)),(Tern (v1,v2,v3))) = Tern (v1,v102,v2) by A925;
hence Tern ((Tern (v1,v102,v2)),(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v104,(Tern (v1,v102,v2))))))) = Tern (v102,(Tern (v1,v102,v2)),(Tern (v1,v2,v3))) by A1219; :: thesis: verum
end;
A1312: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v4,(Tern (v1,v5,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2)
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v4,(Tern (v1,v5,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2)
Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) = Tern (v0,v1,v2) by A925;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v4,(Tern (v1,v5,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2) by A1309; :: thesis: verum
end;
A1315: for v103, v2, v101, v102, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102)))))),(Tern (v101,v102,v103)),(Tern (v101,v102,(Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102))))))))) = Tern (v101,v3,v102)
proof
let v103, v2, v101, v102, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102)))))),(Tern (v101,v102,v103)),(Tern (v101,v102,(Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102))))))))) = Tern (v101,v3,v102)
Tern (v101,v102,(Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102))))))) = Tern (v101,v3,v102) by A1305;
hence Tern ((Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102)))))),(Tern (v101,v102,v103)),(Tern (v101,v102,(Tern (v2,v3,(Tern (v101,v3,(Tern (v3,v4,v102))))))))) = Tern (v101,v3,v102) by A729; :: thesis: verum
end;
A1318: for v5, v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,(Tern (v1,v3,v4)),v2)))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v2,v1,(Tern (v1,v3,v4))))))))) = Tern (v2,v1,v4)
proof
let v5, v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,(Tern (v1,v3,v4)),v2)))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v2,v1,(Tern (v1,v3,v4))))))))) = Tern (v2,v1,v4)
Tern (v1,(Tern (v1,v3,v4)),v2) = Tern (v2,v1,(Tern (v1,v3,v4))) by A3;
hence Tern ((Tern (v0,v1,(Tern (v1,(Tern (v1,v3,v4)),v2)))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v2,v1,(Tern (v1,v3,v4))))))))) = Tern (v2,v1,v4) by A1315; :: thesis: verum
end;
A1321: for v5, v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3)))))),(Tern (v4,v3,v5)),(Tern (v4,v3,(Tern (v0,v1,(Tern (v4,v1,(Tern (v1,v2,v3))))))))) = Tern (v4,v1,v3)
proof
let v5, v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3)))))),(Tern (v4,v3,v5)),(Tern (v4,v3,(Tern (v0,v1,(Tern (v4,v1,(Tern (v1,v2,v3))))))))) = Tern (v4,v1,v3)
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v1,v4,(Tern (v1,v2,v3))) by A4;
hence Tern ((Tern (v0,v1,(Tern (v1,v4,(Tern (v1,v2,v3)))))),(Tern (v4,v3,v5)),(Tern (v4,v3,(Tern (v0,v1,(Tern (v4,v1,(Tern (v1,v2,v3))))))))) = Tern (v4,v1,v3) by A1318; :: thesis: verum
end;
A1324: for v5, v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,(Tern (v1,v3,v4)),v2))))))) = Tern (v2,v1,v4)
proof
let v5, v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,(Tern (v1,v3,v4)),v2))))))) = Tern (v2,v1,v4)
Tern (v1,(Tern (v1,v3,v4)),v2) = Tern (v2,v1,(Tern (v1,v3,v4))) by A3;
hence Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,(Tern (v1,v3,v4)),v2))))))) = Tern (v2,v1,v4) by A1321; :: thesis: verum
end;
A1326: for v5, v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))))) = Tern (v2,v1,v4)
proof
let v5, v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))))) = Tern (v2,v1,v4)
Tern (v1,(Tern (v1,v3,v4)),v2) = Tern (v1,v2,(Tern (v1,v3,v4))) by A4;
hence Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))))) = Tern (v2,v1,v4) by A1324; :: thesis: verum
end;
A1328: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v2,v1,v4)
proof
now :: thesis: for v5, v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v2,v1,v4)
let v5, v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v2,v1,v4)
Tern ((Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4)))))),(Tern (v2,v4,v5)),(Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))))) = Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))) by A729;
hence Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v2,v1,v4) by A1326; :: thesis: verum
end;
hence for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v2,v4,(Tern (v0,v1,(Tern (v1,v2,(Tern (v1,v3,v4))))))) = Tern (v2,v1,v4) ; :: thesis: verum
end;
A1331: for v2, v0, v1, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v0,(Tern (v3,v4,v1))))))) = Tern (v3,v1,v0)
proof
let v2, v0, v1, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v0,(Tern (v3,v4,v1))))))) = Tern (v3,v1,v0)
Tern (v3,v1,v0) = Tern (v0,v3,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v0,(Tern (v3,v4,v1))))))) = Tern (v3,v1,v0) by A1328; :: thesis: verum
end;
A1333: for v2, v0, v1, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v0,(Tern (v3,v4,v1))))))) = Tern (v3,v0,v1)
proof
let v2, v0, v1, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v0,(Tern (v3,v4,v1))))))) = Tern (v3,v0,v1)
Tern (v3,v1,v0) = Tern (v3,v0,v1) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v3,v0,(Tern (v3,v4,v1))))))) = Tern (v3,v0,v1) by A1331; :: thesis: verum
end;
A1335: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v3)))))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v3)))))
Tern (v3,v4,(Tern (v0,v2,v3))) = Tern (v0,v3,(Tern (v2,v3,v4))) by A708;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v3))))) by A280; :: thesis: verum
end;
A1340: for v100, v4, v103, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v103,v4))))) = Tern (v103,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v100,v4)))))
proof
let v100, v4, v103, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v103,v4))))) = Tern (v103,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v100,v4)))))
Tern (v103,(Tern (v102,v103,v4)),(Tern (v102,v100,(Tern (v102,v103,v4))))) = Tern (v103,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v100,v4))))) by A328;
hence Tern (v100,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v103,v4))))) = Tern (v103,(Tern (v102,v103,v4)),(Tern (v102,v103,(Tern (v102,v100,v4))))) by A1033; :: thesis: verum
end;
A1343: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v0,v3)))))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v0,v3)))))
Tern (v1,v2,(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A74;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v0,v3))))) by A1340; :: thesis: verum
end;
A1345: for v2, v3, v0, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,v3) = Tern (v2,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v0,v3)))))
proof
let v2, v3, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,v3) = Tern (v2,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v0,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A34;
hence Tern (v1,v2,v3) = Tern (v2,(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v1,v0,v3))))) by A1343; :: thesis: verum
end;
A1348: for v1, v0, v2, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v2,v0)))))
proof
let v1, v0, v2, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v2,v0)))))
Tern (v3,v2,v0) = Tern (v0,v3,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v2,v0))))) by A1345; :: thesis: verum
end;
A1350: for v1, v2, v0, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v0,v2)))))
proof
let v1, v2, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v0,v2)))))
Tern (v3,v2,v0) = Tern (v3,v0,v2) by A4;
hence Tern (v0,v1,v2) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v0,v2))))) by A1348; :: thesis: verum
end;
A1352: for v1, v2, v0, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v1,(Tern (v3,v0,v2)),v2)))
proof
let v1, v2, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v1,(Tern (v3,v0,v2)),v2)))
Tern (v1,(Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v3,v0,v2))))) = Tern (v0,v1,(Tern (v1,(Tern (v3,v0,v2)),v2))) by A1233;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v1,(Tern (v3,v0,v2)),v2))) by A1350; :: thesis: verum
end;
A1354: for v1, v2, v0, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v1,v2,(Tern (v3,v0,v2)))))
proof
let v1, v2, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v1,v2,(Tern (v3,v0,v2)))))
Tern (v1,(Tern (v3,v0,v2)),v2) = Tern (v1,v2,(Tern (v3,v0,v2))) by A4;
hence Tern (v0,v1,v2) = Tern (v0,v1,(Tern (v1,v2,(Tern (v3,v0,v2))))) by A1352; :: thesis: verum
end;
A1358: for v100, v102, v103, v3 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v3,v103,v102)),(Tern (v100,v102,(Tern (v103,v100,(Tern (v3,v103,v102))))))) = Tern (v103,v100,v102)
proof
let v100, v102, v103, v3 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v3,v103,v102)),(Tern (v100,v102,(Tern (v103,v100,(Tern (v3,v103,v102))))))) = Tern (v103,v100,v102)
Tern (v103,v100,(Tern (v100,v102,(Tern (v3,v103,v102))))) = Tern (v103,v100,v102) by A1354;
hence Tern (v100,(Tern (v3,v103,v102)),(Tern (v100,v102,(Tern (v103,v100,(Tern (v3,v103,v102))))))) = Tern (v103,v100,v102) by A495; :: thesis: verum
end;
A1361: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,(Tern (v1,v2,v3)),v2))))) = Tern (v2,v0,v3)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,(Tern (v1,v2,v3)),v2))))) = Tern (v2,v0,v3)
Tern (v0,(Tern (v1,v2,v3)),v2) = Tern (v2,v0,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,(Tern (v1,v2,v3)),v2))))) = Tern (v2,v0,v3) by A1358; :: thesis: verum
end;
A1363: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern (v2,v0,v3)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern (v2,v0,v3)
Tern (v0,(Tern (v1,v2,v3)),v2) = Tern (v0,v2,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern (v2,v0,v3) by A1361; :: thesis: verum
end;
A1365: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v2,v0,v3)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v2,v0,v3)
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))))) = Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))) by A78;
hence Tern (v0,v3,(Tern (v0,v2,(Tern (v1,v2,v3))))) = Tern (v2,v0,v3) by A1363; :: thesis: verum
end;
A1368: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v1,v2)
proof
let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v1,v2)
Tern (v0,v1,v2) = Tern (v2,v0,v1) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v1,v2) by A1365; :: thesis: verum
end;
A1370: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v2,v1)
proof
let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v2,v1)
Tern (v0,v1,v2) = Tern (v0,v2,v1) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v2,v1))))) = Tern (v0,v2,v1) by A1368; :: thesis: verum
end;
A1373: for v101, v103, v3, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v102,v3,v103)),(Tern (v101,v102,v103)),(Tern (v101,v102,v103))) = Tern (v101,(Tern (v102,v3,v103)),(Tern (v101,v102,v103)))
proof
let v101, v103, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v102,v3,v103)),(Tern (v101,v102,v103)),(Tern (v101,v102,v103))) = Tern (v101,(Tern (v102,v3,v103)),(Tern (v101,v102,v103)))
Tern (v101,v102,(Tern (v101,v103,(Tern (v102,v3,v103))))) = Tern (v101,v102,v103) by A836;
hence Tern ((Tern (v102,v3,v103)),(Tern (v101,v102,v103)),(Tern (v101,v102,v103))) = Tern (v101,(Tern (v102,v3,v103)),(Tern (v101,v102,v103))) by A352; :: thesis: verum
end;
A1376: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v0)),(Tern (v3,v0,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v0)),(Tern (v3,v0,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
Tern (v3,v0,v2) = Tern (v2,v3,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,v0)),(Tern (v3,v0,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))) by A1373; :: thesis: verum
end;
A1378: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v3,v0,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v3,v0,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v3,v0,v2))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))) by A1376; :: thesis: verum
end;
A1380: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v2,v3,v0))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v2,v3,v0))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
Tern (v3,v0,v2) = Tern (v2,v3,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v2,v3,v0))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))) by A1378; :: thesis: verum
end;
A1382: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v3))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v3))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v3))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))) by A1380; :: thesis: verum
end;
A1384: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v2,v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3) by A34;
hence Tern (v0,v2,v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))) by A1382; :: thesis: verum
end;
A1387: for v2, v1, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v1,v2,v0)))
proof
let v2, v1, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v1,v2,v0)))
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v1,v2,v0))) by A1384; :: thesis: verum
end;
A1389: for v2, v1, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v0,v1,v2)))
proof
let v2, v1, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v0,v1,v2)))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v0,v1,v2))) by A1387; :: thesis: verum
end;
A1394: for v3, v102, v101, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v3,v1,v2)),(Tern (v101,v102,(Tern (v1,v2,v101)))),(Tern (v101,v102,(Tern (v1,v2,v101))))) = Tern (v101,(Tern (v3,v1,v2)),(Tern (v101,v102,(Tern (v1,v2,v101)))))
proof
let v3, v102, v101, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,v1,v2)),(Tern (v101,v102,(Tern (v1,v2,v101)))),(Tern (v101,v102,(Tern (v1,v2,v101))))) = Tern (v101,(Tern (v3,v1,v2)),(Tern (v101,v102,(Tern (v1,v2,v101)))))
Tern (v101,(Tern (v1,v2,v101)),(Tern (v3,v1,v2))) = Tern (v1,v2,v101) by A1121;
hence Tern ((Tern (v3,v1,v2)),(Tern (v101,v102,(Tern (v1,v2,v101)))),(Tern (v101,v102,(Tern (v1,v2,v101))))) = Tern (v101,(Tern (v3,v1,v2)),(Tern (v101,v102,(Tern (v1,v2,v101))))) by A352; :: thesis: verum
end;
A1397: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v1,v2,v3))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v1,v2,v3)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,v4,(Tern (v1,v2,v3))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v1,v2,v3)))))
Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v1,v2,v3)))),(Tern (v3,v4,(Tern (v1,v2,v3))))) = Tern (v3,v4,(Tern (v1,v2,v3))) by A34;
hence Tern (v3,v4,(Tern (v1,v2,v3))) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v1,v2,v3))))) by A1394; :: thesis: verum
end;
A1403: for v101, v3, v103, v4, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v102,v3,(Tern (v102,v4,v103)))),(Tern (v101,v102,v103)),(Tern (v101,v102,v103))) = Tern (v101,(Tern (v102,v3,(Tern (v102,v4,v103)))),(Tern (v101,v102,v103)))
proof
let v101, v3, v103, v4, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v102,v3,(Tern (v102,v4,v103)))),(Tern (v101,v102,v103)),(Tern (v101,v102,v103))) = Tern (v101,(Tern (v102,v3,(Tern (v102,v4,v103)))),(Tern (v101,v102,v103)))
Tern (v101,v102,(Tern (v101,v103,(Tern (v102,v3,(Tern (v102,v4,v103))))))) = Tern (v101,v102,v103) by A861;
hence Tern ((Tern (v102,v3,(Tern (v102,v4,v103)))),(Tern (v101,v102,v103)),(Tern (v101,v102,v103))) = Tern (v101,(Tern (v102,v3,(Tern (v102,v4,v103)))),(Tern (v101,v102,v103))) by A352; :: thesis: verum
end;
A1406: for v4, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v3,v4,v0)),(Tern (v4,v0,v3))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
proof
let v4, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v3,v4,v0)),(Tern (v4,v0,v3))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
Tern (v4,v0,v3) = Tern (v3,v4,v0) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v3,v4,v0)),(Tern (v4,v0,v3))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3))) by A1403; :: thesis: verum
end;
A1408: for v4, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,v0,v3))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
proof
let v4, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,v0,v3))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
Tern (v3,v4,v0) = Tern (v0,v3,v4) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,v0,v3))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3))) by A1406; :: thesis: verum
end;
A1410: for v4, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v3,v4,v0))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
proof
let v4, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v3,v4,v0))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
Tern (v4,v0,v3) = Tern (v3,v4,v0) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v3,v4,v0))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3))) by A1408; :: thesis: verum
end;
A1412: for v4, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v0,v3,v4))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
proof
let v4, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v0,v3,v4))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
Tern (v3,v4,v0) = Tern (v0,v3,v4) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v0,v3,v4))) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3))) by A1410; :: thesis: verum
end;
A1414: for v4, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v3,v4) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
proof
let v4, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,v4) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3)))
Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v0,v3,v4))) = Tern (v0,v3,v4) by A34;
hence Tern (v0,v3,v4) = Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v4,v0,v3))) by A1412; :: thesis: verum
end;
A1417: for v2, v3, v1, v4, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,(Tern (v0,v4,v1)))),(Tern (v1,v2,v0)))
proof
let v2, v3, v1, v4, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,(Tern (v0,v4,v1)))),(Tern (v1,v2,v0)))
Tern (v2,v0,v1) = Tern (v1,v2,v0) by A3;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,(Tern (v0,v4,v1)))),(Tern (v1,v2,v0))) by A1414; :: thesis: verum
end;
A1419: for v2, v3, v1, v4, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,(Tern (v0,v4,v1)))),(Tern (v0,v1,v2)))
proof
let v2, v3, v1, v4, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,(Tern (v0,v4,v1)))),(Tern (v0,v1,v2)))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern (v0,v1,v2) = Tern (v2,(Tern (v0,v3,(Tern (v0,v4,v1)))),(Tern (v0,v1,v2))) by A1417; :: thesis: verum
end;
A1424: for v104, v103, v2, v102 being Element of (BA2TBAA B) holds Tern (v104,(Tern (v102,v2,v103)),(Tern (v102,v103,(Tern ((Tern (v102,v2,v103)),v103,v104))))) = Tern ((Tern (v102,v2,v103)),v103,(Tern (v102,v103,v104)))
proof
let v104, v103, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern (v104,(Tern (v102,v2,v103)),(Tern (v102,v103,(Tern ((Tern (v102,v2,v103)),v103,v104))))) = Tern ((Tern (v102,v2,v103)),v103,(Tern (v102,v103,v104)))
Tern (v104,(Tern (v102,v2,v103)),(Tern (v102,v103,v104))) = Tern (v102,v103,v104) by A1389;
hence Tern (v104,(Tern (v102,v2,v103)),(Tern (v102,v103,(Tern ((Tern (v102,v2,v103)),v103,v104))))) = Tern ((Tern (v102,v2,v103)),v103,(Tern (v102,v103,v104))) by A236; :: thesis: verum
end;
A1427: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v3)),v3))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v3)),v3))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0)))
Tern ((Tern (v1,v2,v3)),v3,v0) = Tern (v0,(Tern (v1,v2,v3)),v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v3)),v3))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0))) by A1424; :: thesis: verum
end;
A1429: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0)))
Tern (v0,(Tern (v1,v2,v3)),v3) = Tern (v0,v3,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0))) by A1427; :: thesis: verum
end;
A1431: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v3,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v3,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,v3,(Tern (v1,v2,v3))) by A753;
hence Tern (v0,v3,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v3,(Tern (v1,v3,v0))) by A1429; :: thesis: verum
end;
A1434: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v2,v1)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v2,v1)))
Tern (v2,v1,v0) = Tern (v0,v2,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v2,v1))) by A1431; :: thesis: verum
end;
A1436: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v1)))
proof
let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v1)))
Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v1))) = Tern ((Tern (v2,v3,v1)),v1,(Tern (v0,v2,v1))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v1))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v1))) by A1434; :: thesis: verum
end;
A1441: for v3, v103, v101, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v2,v3,v101)),(Tern (v101,(Tern (v1,v2,v101)),v103)),(Tern (v101,(Tern (v1,v2,v101)),(Tern (v2,v3,v101))))) = Tern (v1,v101,(Tern (v2,v3,v101)))
proof
let v3, v103, v101, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v2,v3,v101)),(Tern (v101,(Tern (v1,v2,v101)),v103)),(Tern (v101,(Tern (v1,v2,v101)),(Tern (v2,v3,v101))))) = Tern (v1,v101,(Tern (v2,v3,v101)))
Tern (v101,(Tern (v1,v2,v101)),(Tern (v2,v3,v101))) = Tern (v1,v101,(Tern (v2,v3,v101))) by A1436;
hence Tern ((Tern (v2,v3,v101)),(Tern (v101,(Tern (v1,v2,v101)),v103)),(Tern (v101,(Tern (v1,v2,v101)),(Tern (v2,v3,v101))))) = Tern (v1,v101,(Tern (v2,v3,v101))) by A729; :: thesis: verum
end;
A1444: for v1, v4, v0, v3, v2 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,(Tern (v2,v3,v0)),v4)),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2)))
proof
let v1, v4, v0, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,(Tern (v2,v3,v0)),v4)),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2)))
Tern (v3,v0,v2) = Tern (v2,v3,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,(Tern (v2,v3,v0)),v4)),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2))) by A1441; :: thesis: verum
end;
A1446: for v1, v4, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,(Tern (v0,v2,v3)),v4)),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2)))
proof
let v1, v4, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,(Tern (v0,v2,v3)),v4)),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,(Tern (v0,v2,v3)),v4)),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2))) by A1444; :: thesis: verum
end;
A1448: for v1, v4, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,v4,(Tern (v0,v2,v3)))),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2)))
proof
let v1, v4, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,v4,(Tern (v0,v2,v3)))),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2)))
Tern (v2,(Tern (v0,v2,v3)),v4) = Tern (v2,v4,(Tern (v0,v2,v3))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,v4,(Tern (v0,v2,v3)))),(Tern (v2,(Tern (v3,v0,v2)),(Tern (v0,v1,v2))))) = Tern (v3,v2,(Tern (v0,v1,v2))) by A1446; :: thesis: verum
end;
A1451: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v2,v4,v0)),(Tern (v0,v1,v2))))) = Tern (v4,v2,(Tern (v0,v1,v2)))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v2,v4,v0)),(Tern (v0,v1,v2))))) = Tern (v4,v2,(Tern (v0,v1,v2)))
Tern (v4,v0,v2) = Tern (v2,v4,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v2,v4,v0)),(Tern (v0,v1,v2))))) = Tern (v4,v2,(Tern (v0,v1,v2))) by A1448; :: thesis: verum
end;
A1453: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))))) = Tern (v4,v2,(Tern (v0,v1,v2)))
proof
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))))) = Tern (v4,v2,(Tern (v0,v1,v2)))
Tern (v2,v4,v0) = Tern (v0,v2,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))))) = Tern (v4,v2,(Tern (v0,v1,v2))) by A1451; :: thesis: verum
end;
A1455: for v1, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))) = Tern (v4,v2,(Tern (v0,v1,v2)))
proof
now :: thesis: for v1, v3, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))) = Tern (v4,v2,(Tern (v0,v1,v2)))
let v1, v3, v4, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))) = Tern (v4,v2,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v2,v3,(Tern (v0,v2,v4)))),(Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))))) = Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))) by A1389;
hence Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))) = Tern (v4,v2,(Tern (v0,v1,v2))) by A1453; :: thesis: verum
end;
hence for v1, v4, v2, v0 being Element of (BA2TBAA B) holds Tern (v2,(Tern (v0,v2,v4)),(Tern (v0,v1,v2))) = Tern (v4,v2,(Tern (v0,v1,v2))) ; :: thesis: verum
end;
A1458: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v0,v2)),(Tern (v1,v3,v0))) = Tern (v0,(Tern (v1,v3,v0)),v2)
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v0,v2)),(Tern (v1,v3,v0))) = Tern (v0,(Tern (v1,v3,v0)),v2)
Tern (v0,(Tern (v1,v3,v0)),v2) = Tern (v2,v0,(Tern (v1,v3,v0))) by A3;
hence Tern (v0,(Tern (v1,v0,v2)),(Tern (v1,v3,v0))) = Tern (v0,(Tern (v1,v3,v0)),v2) by A1455; :: thesis: verum
end;
A1460: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v0,v2)),(Tern (v1,v3,v0))) = Tern (v0,v2,(Tern (v1,v3,v0)))
proof
let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v0,v2)),(Tern (v1,v3,v0))) = Tern (v0,v2,(Tern (v1,v3,v0)))
Tern (v0,(Tern (v1,v3,v0)),v2) = Tern (v0,v2,(Tern (v1,v3,v0))) by A4;
hence Tern (v0,(Tern (v1,v0,v2)),(Tern (v1,v3,v0))) = Tern (v0,v2,(Tern (v1,v3,v0))) by A1458; :: thesis: verum
end;
A1463: for v103, v102, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v4,v102)),(Tern (v102,(Tern (v1,v4,v102)),(Tern (v102,(Tern (v1,v2,(Tern (v1,v3,v4)))),v103))))) = Tern (v1,v4,v102)
proof
let v103, v102, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v4,v102)),(Tern (v102,(Tern (v1,v4,v102)),(Tern (v102,(Tern (v1,v2,(Tern (v1,v3,v4)))),v103))))) = Tern (v1,v4,v102)
Tern (v102,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v4,v102))) = Tern (v1,v4,v102) by A1419;
hence Tern ((Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v4,v102)),(Tern (v102,(Tern (v1,v4,v102)),(Tern (v102,(Tern (v1,v2,(Tern (v1,v3,v4)))),v103))))) = Tern (v1,v4,v102) by A693; :: thesis: verum
end;
A1466: for v4, v5, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,(Tern (v0,v2,v3))))))))) = Tern (v0,v3,v4)
proof
let v4, v5, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,(Tern (v0,v2,v3))))))))) = Tern (v0,v3,v4)
Tern (v4,(Tern (v0,v1,(Tern (v0,v2,v3)))),v5) = Tern (v4,v5,(Tern (v0,v1,(Tern (v0,v2,v3))))) by A4;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,(Tern (v0,v2,v3))))))))) = Tern (v0,v3,v4) by A1463; :: thesis: verum
end;
A1469: for v3, v102, v103, v2, v101, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v101,v2)),(Tern (v101,v102,v103)),(Tern (v1,v101,v2))) = Tern ((Tern (v1,v101,v2)),(Tern (v1,v2,v3)),(Tern (v101,v102,(Tern (v101,v103,(Tern (v1,v101,v2)))))))
proof
let v3, v102, v103, v2, v101, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v101,v2)),(Tern (v101,v102,v103)),(Tern (v1,v101,v2))) = Tern ((Tern (v1,v101,v2)),(Tern (v1,v2,v3)),(Tern (v101,v102,(Tern (v101,v103,(Tern (v1,v101,v2)))))))
Tern (v101,(Tern (v1,v101,v2)),(Tern (v1,v2,v3))) = Tern (v1,v101,v2) by A925;
hence Tern ((Tern (v1,v101,v2)),(Tern (v101,v102,v103)),(Tern (v1,v101,v2))) = Tern ((Tern (v1,v101,v2)),(Tern (v1,v2,v3)),(Tern (v101,v102,(Tern (v101,v103,(Tern (v1,v101,v2))))))) by A402; :: thesis: verum
end;
A1472: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
proof
now :: thesis: for v5, v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
let v5, v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v5)),(Tern (v1,v3,(Tern (v1,v4,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2) by A1312;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A1469; :: thesis: verum
end;
hence for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v3,v4)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) ; :: thesis: verum
end;
A1475: for v104, v101, v4, v3, v103 being Element of (BA2TBAA B) holds Tern ((Tern (v103,v3,v4)),v101,(Tern ((Tern (v103,v3,v4)),v103,v104))) = Tern ((Tern ((Tern (v103,v3,v4)),v103,v104)),(Tern (v103,v3,v4)),(Tern ((Tern (v103,v3,v4)),v103,(Tern ((Tern (v103,v3,v4)),v101,v104)))))
proof
let v104, v101, v4, v3, v103 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v103,v3,v4)),v101,(Tern ((Tern (v103,v3,v4)),v103,v104))) = Tern ((Tern ((Tern (v103,v3,v4)),v103,v104)),(Tern (v103,v3,v4)),(Tern ((Tern (v103,v3,v4)),v103,(Tern ((Tern (v103,v3,v4)),v101,v104)))))
Tern ((Tern ((Tern (v103,v3,v4)),v103,v104)),(Tern (v103,v3,v4)),(Tern ((Tern (v103,v3,v4)),v103,v104))) = Tern ((Tern (v103,v3,v4)),v103,v104) by A1472;
hence Tern ((Tern (v103,v3,v4)),v101,(Tern ((Tern (v103,v3,v4)),v103,v104))) = Tern ((Tern ((Tern (v103,v3,v4)),v103,v104)),(Tern (v103,v3,v4)),(Tern ((Tern (v103,v3,v4)),v103,(Tern ((Tern (v103,v3,v4)),v101,v104))))) by A162; :: thesis: verum
end;
A1478: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v0))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v0))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
Tern ((Tern (v0,v1,v2)),v0,v4) = Tern (v4,(Tern (v0,v1,v2)),v0) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v0))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4))))) by A1475; :: thesis: verum
end;
A1480: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
Tern (v4,(Tern (v0,v1,v2)),v0) = Tern (v0,v4,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4))))) by A1478; :: thesis: verum
end;
A1482: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4)))))
Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v4,(Tern (v0,v1,v2))))) by A3;
hence Tern (v3,(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),v3,v4))))) by A1480; :: thesis: verum
end;
A1485: for v2, v0, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern ((Tern ((Tern (v1,v3,v4)),v1,v2)),(Tern (v1,v3,v4)),(Tern ((Tern (v1,v3,v4)),v1,(Tern ((Tern (v1,v3,v4)),v0,v2)))))
proof
let v2, v0, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern ((Tern ((Tern (v1,v3,v4)),v1,v2)),(Tern (v1,v3,v4)),(Tern ((Tern (v1,v3,v4)),v1,(Tern ((Tern (v1,v3,v4)),v0,v2)))))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,v4)))),(Tern (v1,v3,v4))) = Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern (v0,(Tern (v1,v3,v4)),(Tern (v1,v2,(Tern (v1,v3,v4))))) = Tern ((Tern ((Tern (v1,v3,v4)),v1,v2)),(Tern (v1,v3,v4)),(Tern ((Tern (v1,v3,v4)),v1,(Tern ((Tern (v1,v3,v4)),v0,v2))))) by A1482; :: thesis: verum
end;
A1488: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v4,(Tern (v1,v2,v3)),v1)),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v4)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v4,(Tern (v1,v2,v3)),v1)),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v4)))))
Tern ((Tern (v1,v2,v3)),v1,v4) = Tern (v4,(Tern (v1,v2,v3)),v1) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v4,(Tern (v1,v2,v3)),v1)),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v4))))) by A1485; :: thesis: verum
end;
A1490: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v4)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v4)))))
Tern (v4,(Tern (v1,v2,v3)),v1) = Tern (v1,v4,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern ((Tern (v1,v2,v3)),v0,v4))))) by A1488; :: thesis: verum
end;
A1492: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern (v4,(Tern (v1,v2,v3)),v0)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern (v4,(Tern (v1,v2,v3)),v0)))))
Tern ((Tern (v1,v2,v3)),v0,v4) = Tern (v4,(Tern (v1,v2,v3)),v0) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern (v4,(Tern (v1,v2,v3)),v0))))) by A1490; :: thesis: verum
end;
A1494: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v4,(Tern (v1,v2,v3)),v0) = Tern (v0,v4,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v1,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1492; :: thesis: verum
end;
A1496: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))))
Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v1,(Tern (v0,v4,(Tern (v1,v2,v3))))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) by A1494; :: thesis: verum
end;
A1498: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1496; :: thesis: verum
end;
A1500: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))))
Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A558;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) by A1498; :: thesis: verum
end;
A1502: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))),(Tern (v1,v4,(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))),(Tern (v1,v4,(Tern (v1,v2,v3)))))
Tern ((Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))),(Tern (v1,v4,(Tern (v1,v2,v3))))) by A1500; :: thesis: verum
end;
A1504: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))))
Tern ((Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) by A1502; :: thesis: verum
end;
A1506: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))))
Tern ((Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3)))),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) by A1287;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) by A1504; :: thesis: verum
end;
A1508: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v1,(Tern (v0,v4,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1506; :: thesis: verum
end;
A1510: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))))
Tern (v1,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A558;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) by A1508; :: thesis: verum
end;
A1515: for v104, v101, v4, v3, v103 being Element of (BA2TBAA B) holds Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),v101,(Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104))))) = Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),v101,(Tern (v103,v3,v4)))
proof
let v104, v101, v4, v3, v103 be Element of (BA2TBAA B); :: thesis: Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),v101,(Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104))))) = Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),v101,(Tern (v103,v3,v4)))
Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),(Tern (v103,v3,v4)),(Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104))))) = Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104))) by A1472;
hence Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),v101,(Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104))))) = Tern ((Tern ((Tern (v103,v3,v4)),v103,(Tern (v101,(Tern (v103,v3,v4)),v104)))),v101,(Tern (v103,v3,v4))) by A632; :: thesis: verum
end;
A1518: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2)))
Tern (v3,(Tern (v0,v1,v2)),v4) = Tern (v3,v4,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,v4,(Tern (v0,v1,v2)))))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2))) by A1515; :: thesis: verum
end;
A1520: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,v4,(Tern (v0,v1,v2))))) by A3;
hence Tern ((Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2))) by A1518; :: thesis: verum
end;
A1523: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4)))))),v1,(Tern ((Tern (v0,v3,v4)),v0,(Tern (v1,(Tern (v0,v3,v4)),v2))))) = Tern ((Tern ((Tern (v0,v3,v4)),v0,(Tern (v1,(Tern (v0,v3,v4)),v2)))),v1,(Tern (v0,v3,v4)))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4)))))),v1,(Tern ((Tern (v0,v3,v4)),v0,(Tern (v1,(Tern (v0,v3,v4)),v2))))) = Tern ((Tern ((Tern (v0,v3,v4)),v0,(Tern (v1,(Tern (v0,v3,v4)),v2)))),v1,(Tern (v0,v3,v4)))
Tern (v0,(Tern (v1,v2,(Tern (v0,v3,v4)))),(Tern (v0,v3,v4))) = Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4))))) by A4;
hence Tern ((Tern (v0,(Tern (v0,v3,v4)),(Tern (v1,v2,(Tern (v0,v3,v4)))))),v1,(Tern ((Tern (v0,v3,v4)),v0,(Tern (v1,(Tern (v0,v3,v4)),v2))))) = Tern ((Tern ((Tern (v0,v3,v4)),v0,(Tern (v1,(Tern (v0,v3,v4)),v2)))),v1,(Tern (v0,v3,v4))) by A1520; :: thesis: verum
end;
A1526: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2)))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A558;
hence Tern ((Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),v3,(Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4))))) = Tern ((Tern ((Tern (v0,v1,v2)),v0,(Tern (v3,(Tern (v0,v1,v2)),v4)))),v3,(Tern (v0,v1,v2))) by A1523; :: thesis: verum
end;
A1529: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
Tern (v3,(Tern (v0,v2,v1)),v4) = Tern (v3,v4,(Tern (v0,v2,v1))) by A4;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1))) by A1526; :: thesis: verum
end;
A1531: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))) = Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1))))) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1))) by A1529; :: thesis: verum
end;
A1533: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))) = Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))) by A4;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1))) by A1531; :: thesis: verum
end;
A1535: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) by A558;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1))) by A1533; :: thesis: verum
end;
A1537: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1)))
Tern (v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) by A3;
hence Tern (v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,(Tern (v0,v2,v1)),v4)))),v3,(Tern (v0,v2,v1))) by A1535; :: thesis: verum
end;
A1540: for v0, v4, v2, v3, v1 being Element of (BA2TBAA B) holds Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))) = Tern ((Tern ((Tern (v1,v3,v2)),v1,(Tern (v0,(Tern (v1,v3,v2)),v4)))),v0,(Tern (v1,v3,v2)))
proof
let v0, v4, v2, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))) = Tern ((Tern ((Tern (v1,v3,v2)),v1,(Tern (v0,(Tern (v1,v3,v2)),v4)))),v0,(Tern (v1,v3,v2)))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2)))))))),(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))))) = Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))) by A34;
hence Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))) = Tern ((Tern ((Tern (v1,v3,v2)),v1,(Tern (v0,(Tern (v1,v3,v2)),v4)))),v0,(Tern (v1,v3,v2))) by A1537; :: thesis: verum
end;
A1543: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1)))))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1)))))),v3,(Tern (v0,v2,v1)))
Tern (v3,(Tern (v0,v2,v1)),v4) = Tern (v3,v4,(Tern (v0,v2,v1))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1)))))),v3,(Tern (v0,v2,v1))) by A1540; :: thesis: verum
end;
A1545: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)))),v3,(Tern (v0,v2,v1)))
Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))) = Tern ((Tern (v0,v2,v1)),v0,(Tern (v3,v4,(Tern (v0,v2,v1))))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)))),v3,(Tern (v0,v2,v1))) by A1543; :: thesis: verum
end;
A1547: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))))),v3,(Tern (v0,v2,v1)))
Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))) = Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))))),v3,(Tern (v0,v2,v1))) by A1545; :: thesis: verum
end;
A1549: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v2,v1)))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v2,v1)))
Tern (v0,(Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1))))) = Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) by A558;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v2,v1))) by A1547; :: thesis: verum
end;
A1551: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3)
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3)
Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3,(Tern (v0,v2,v1))) = Tern ((Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3) by A1549; :: thesis: verum
end;
A1553: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))))
Tern ((Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1)))))))),v3) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) by A1551; :: thesis: verum
end;
A1558: for v4, v2, v3, v100, v1 being Element of (BA2TBAA B) holds Tern (v4,v100,(Tern (v1,v2,(Tern (v1,v100,v3))))) = Tern (v100,(Tern (v4,v1,v100)),(Tern (v1,v2,v3)))
proof
let v4, v2, v3, v100, v1 be Element of (BA2TBAA B); :: thesis: Tern (v4,v100,(Tern (v1,v2,(Tern (v1,v100,v3))))) = Tern (v100,(Tern (v4,v1,v100)),(Tern (v1,v2,v3)))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v4,v1,v100))) = Tern (v4,v100,(Tern (v1,v2,(Tern (v1,v100,v3))))) by A419;
hence Tern (v4,v100,(Tern (v1,v2,(Tern (v1,v100,v3))))) = Tern (v100,(Tern (v4,v1,v100)),(Tern (v1,v2,v3))) by A4; :: thesis: verum
end;
A1561: for v0, v3, v2, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v2))))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v4)))
proof
let v0, v3, v2, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v2))))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v4)))
Tern (v1,v4,v2) = Tern (v2,v1,v4) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v2))))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v4))) by A1558; :: thesis: verum
end;
A1563: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v4)))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v4)))
Tern (v1,v4,v2) = Tern (v1,v2,v4) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v2,v1)),(Tern (v2,v3,v4))) by A1561; :: thesis: verum
end;
A1565: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v2,v3,v4)))
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v2,v3,v4)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v2,v4))))) = Tern (v1,(Tern (v0,v1,v2)),(Tern (v2,v3,v4))) by A1563; :: thesis: verum
end;
A1570: for v104, v101, v3, v2, v103 being Element of (BA2TBAA B) holds Tern ((Tern (v103,v2,v3)),v101,(Tern ((Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v103,v104))))) = Tern ((Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,(Tern (v103,(Tern ((Tern (v103,v2,v3)),v101,v104)),v3)))))
proof
let v104, v101, v3, v2, v103 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v103,v2,v3)),v101,(Tern ((Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v103,v104))))) = Tern ((Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,(Tern (v103,(Tern ((Tern (v103,v2,v3)),v101,v104)),v3)))))
Tern ((Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v103,(Tern ((Tern (v103,v2,v3)),v101,v104))))) = Tern ((Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,(Tern (v103,(Tern ((Tern (v103,v2,v3)),v101,v104)),v3))))) by A419;
hence Tern ((Tern (v103,v2,v3)),v101,(Tern ((Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v103,v104))))) = Tern ((Tern (v103,v2,v3)),(Tern ((Tern (v103,v2,v3)),v101,v104)),(Tern (v103,v2,(Tern (v103,(Tern ((Tern (v103,v2,v3)),v101,v104)),v3))))) by A162; :: thesis: verum
end;
A1573: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,v4))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,v4))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern ((Tern (v0,v1,v2)),v3,v4) = Tern (v4,(Tern (v0,v1,v2)),v3) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,v4))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1570; :: thesis: verum
end;
A1575: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,v4))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,v4))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern (v4,(Tern (v0,v1,v2)),v3) = Tern (v3,v4,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v0,v4))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1573; :: thesis: verum
end;
A1577: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v4,(Tern (v0,v1,v2)),v0))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v4,(Tern (v0,v1,v2)),v0))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern ((Tern (v0,v1,v2)),v0,v4) = Tern (v4,(Tern (v0,v1,v2)),v0) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v4,(Tern (v0,v1,v2)),v0))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1575; :: thesis: verum
end;
A1579: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern (v4,(Tern (v0,v1,v2)),v0) = Tern (v0,v4,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1577; :: thesis: verum
end;
A1581: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2))))) by A3;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1579; :: thesis: verum
end;
A1583: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,(Tern (v0,v1,v2)))),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) by A1269;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1581; :: thesis: verum
end;
A1585: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A558;
hence Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1583; :: thesis: verum
end;
A1587: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2)))))
Tern (v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) by A3;
hence Tern (v3,(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2)))))))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) by A1585; :: thesis: verum
end;
A1590: for v0, v4, v2, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v3,v2)),(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))))) = Tern ((Tern (v1,v3,v2)),(Tern ((Tern (v1,v3,v2)),v0,v4)),(Tern (v1,v3,(Tern (v1,(Tern ((Tern (v1,v3,v2)),v0,v4)),v2)))))
proof
let v0, v4, v2, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v3,v2)),(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))))) = Tern ((Tern (v1,v3,v2)),(Tern ((Tern (v1,v3,v2)),v0,v4)),(Tern (v1,v3,(Tern (v1,(Tern ((Tern (v1,v3,v2)),v0,v4)),v2)))))
Tern (v0,(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2)))))))),(Tern (v1,v3,v2))) = Tern (v0,(Tern (v1,v3,v2)),(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))))) by A4;
hence Tern (v0,(Tern (v1,v3,v2)),(Tern (v1,v2,(Tern (v1,v3,(Tern (v0,v4,(Tern (v1,v3,v2))))))))) = Tern ((Tern (v1,v3,v2)),(Tern ((Tern (v1,v3,v2)),v0,v4)),(Tern (v1,v3,(Tern (v1,(Tern ((Tern (v1,v3,v2)),v0,v4)),v2))))) by A1587; :: thesis: verum
end;
A1593: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v0,v4)),(Tern (v1,v2,(Tern (v1,(Tern ((Tern (v1,v2,v3)),v0,v4)),v3)))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v0,v4)),(Tern (v1,v2,(Tern (v1,(Tern ((Tern (v1,v2,v3)),v0,v4)),v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1553;
hence Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),(Tern ((Tern (v1,v2,v3)),v0,v4)),(Tern (v1,v2,(Tern (v1,(Tern ((Tern (v1,v2,v3)),v0,v4)),v3))))) by A1590; :: thesis: verum
end;
A1596: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),v3)),(Tern (v0,v2,(Tern (v0,(Tern ((Tern (v0,v2,v1)),v3,v4)),v1)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),v3)),(Tern (v0,v2,(Tern (v0,(Tern ((Tern (v0,v2,v1)),v3,v4)),v1)))))
Tern ((Tern (v0,v2,v1)),v3,v4) = Tern (v4,(Tern (v0,v2,v1)),v3) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),v3)),(Tern (v0,v2,(Tern (v0,(Tern ((Tern (v0,v2,v1)),v3,v4)),v1))))) by A1593; :: thesis: verum
end;
A1598: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern ((Tern (v0,v2,v1)),v3,v4)),v1)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern ((Tern (v0,v2,v1)),v3,v4)),v1)))))
Tern (v4,(Tern (v0,v2,v1)),v3) = Tern (v3,v4,(Tern (v0,v2,v1))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern ((Tern (v0,v2,v1)),v3,v4)),v1))))) by A1596; :: thesis: verum
end;
A1600: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern (v4,(Tern (v0,v2,v1)),v3)),v1)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern (v4,(Tern (v0,v2,v1)),v3)),v1)))))
Tern ((Tern (v0,v2,v1)),v3,v4) = Tern (v4,(Tern (v0,v2,v1)),v3) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern (v4,(Tern (v0,v2,v1)),v3)),v1))))) by A1598; :: thesis: verum
end;
A1602: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),v1)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),v1)))))
Tern (v4,(Tern (v0,v2,v1)),v3) = Tern (v3,v4,(Tern (v0,v2,v1))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),v1))))) by A1600; :: thesis: verum
end;
A1604: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v1)))))))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v1)))))))))
Tern (v0,(Tern (v3,v4,(Tern (v0,v2,v1)))),v1) = Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v1))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v2,v1))))))))) by A1602; :: thesis: verum
end;
A1609: for v4, v103, v102, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v4,v1,v102)),(Tern (v102,(Tern (v4,v1,v102)),(Tern (v102,(Tern (v1,v2,v3)),v103))))) = Tern (v4,v102,(Tern (v1,v2,(Tern (v1,v102,v3)))))
proof
let v4, v103, v102, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v4,v1,v102)),(Tern (v102,(Tern (v4,v1,v102)),(Tern (v102,(Tern (v1,v2,v3)),v103))))) = Tern (v4,v102,(Tern (v1,v2,(Tern (v1,v102,v3)))))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v4,v1,v102))) = Tern (v4,v102,(Tern (v1,v2,(Tern (v1,v102,v3))))) by A419;
hence Tern ((Tern (v1,v2,v3)),(Tern (v4,v1,v102)),(Tern (v102,(Tern (v4,v1,v102)),(Tern (v102,(Tern (v1,v2,v3)),v103))))) = Tern (v4,v102,(Tern (v1,v2,(Tern (v1,v102,v3))))) by A693; :: thesis: verum
end;
A1612: for v3, v5, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,v3)),(Tern (v4,(Tern (v3,v0,v4)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
proof
let v3, v5, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,v3)),(Tern (v4,(Tern (v3,v0,v4)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
Tern (v0,v4,v3) = Tern (v3,v0,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,v3)),(Tern (v4,(Tern (v3,v0,v4)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2))))) by A1609; :: thesis: verum
end;
A1615: for v4, v5, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,v3)),(Tern (v3,(Tern (v4,v0,v3)),(Tern (v3,(Tern (v0,v1,v2)),v5))))) = Tern (v4,v3,(Tern (v0,v1,(Tern (v0,v3,v2)))))
proof
let v4, v5, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,v3)),(Tern (v3,(Tern (v4,v0,v3)),(Tern (v3,(Tern (v0,v1,v2)),v5))))) = Tern (v4,v3,(Tern (v0,v1,(Tern (v0,v3,v2)))))
Tern (v0,v3,v4) = Tern (v0,v4,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v4,v3)),(Tern (v3,(Tern (v4,v0,v3)),(Tern (v3,(Tern (v0,v1,v2)),v5))))) = Tern (v4,v3,(Tern (v0,v1,(Tern (v0,v3,v2))))) by A1612; :: thesis: verum
end;
A1618: for v3, v5, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v4,v3)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
proof
let v3, v5, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v4,v3)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
Tern (v0,v4,v3) = Tern (v3,v0,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v4,v3)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2))))) by A1615; :: thesis: verum
end;
A1620: for v3, v5, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
proof
let v3, v5, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
Tern (v0,v4,v3) = Tern (v0,v3,v4) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2))))) by A1618; :: thesis: verum
end;
A1622: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,v2))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,v2))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2)))))
Tern (v4,(Tern (v0,v1,v2)),v5) = Tern (v4,v5,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,v2))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v4,v2))))) by A1620; :: thesis: verum
end;
A1624: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,v2))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,v4)))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,v2))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,v4)))))
Tern (v0,v4,v2) = Tern (v0,v2,v4) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,v2))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,v2,v4))))) by A1622; :: thesis: verum
end;
A1627: for v102, v2, v3, v105, v104, v103 being Element of (BA2TBAA B) holds Tern ((Tern (v103,v104,v105)),(Tern (v102,v2,v3)),(Tern ((Tern (v103,v104,v105)),v102,(Tern (v103,v104,(Tern ((Tern (v103,v104,v105)),v103,v105))))))) = Tern ((Tern (v103,v104,v105)),v103,(Tern ((Tern (v103,v104,v105)),(Tern (v103,v104,v105)),(Tern (v102,v2,(Tern (v102,(Tern (v103,v104,v105)),v3)))))))
proof
let v102, v2, v3, v105, v104, v103 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v103,v104,v105)),(Tern (v102,v2,v3)),(Tern ((Tern (v103,v104,v105)),v102,(Tern (v103,v104,(Tern ((Tern (v103,v104,v105)),v103,v105))))))) = Tern ((Tern (v103,v104,v105)),v103,(Tern ((Tern (v103,v104,v105)),(Tern (v103,v104,v105)),(Tern (v102,v2,(Tern (v102,(Tern (v103,v104,v105)),v3)))))))
Tern ((Tern (v103,v104,v105)),(Tern (v102,v2,v3)),(Tern ((Tern (v103,v104,v105)),v102,(Tern (v103,v104,v105))))) = Tern ((Tern (v103,v104,v105)),(Tern (v103,v104,v105)),(Tern (v102,v2,(Tern (v102,(Tern (v103,v104,v105)),v3))))) by A419;
hence Tern ((Tern (v103,v104,v105)),(Tern (v102,v2,v3)),(Tern ((Tern (v103,v104,v105)),v102,(Tern (v103,v104,(Tern ((Tern (v103,v104,v105)),v103,v105))))))) = Tern ((Tern (v103,v104,v105)),v103,(Tern ((Tern (v103,v104,v105)),(Tern (v103,v104,v105)),(Tern (v102,v2,(Tern (v102,(Tern (v103,v104,v105)),v3))))))) by A189; :: thesis: verum
end;
A1630: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v2)),v0))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v2)),v0))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
Tern ((Tern (v0,v1,v2)),v0,v2) = Tern (v2,(Tern (v0,v1,v2)),v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v2)),v0))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5))))))) by A1627; :: thesis: verum
end;
A1632: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v2))))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v2))))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
Tern (v2,(Tern (v0,v1,v2)),v0) = Tern (v0,v2,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v0,v2,(Tern (v0,v1,v2))))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5))))))) by A1630; :: thesis: verum
end;
A1634: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
Tern (v0,v2,(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A63;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,(Tern (v0,v1,v2))))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5))))))) by A1632; :: thesis: verum
end;
A1636: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
Tern (v0,v1,(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A74;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5))))))) by A1634; :: thesis: verum
end;
A1638: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5))))))) by A1636; :: thesis: verum
end;
A1640: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5)))))))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A34;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,(Tern (v0,v1,v2)),v5))))))) by A1638; :: thesis: verum
end;
A1642: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2)))))))))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2)))))))))
Tern (v3,(Tern (v0,v1,v2)),v5) = Tern (v3,v5,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2))))))))) by A1640; :: thesis: verum
end;
A1644: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v0,v1,v2)))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2))))))) = Tern (v0,v1,v2) by A2;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v0,v1,v2))) by A1642; :: thesis: verum
end;
A1646: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2)))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2)))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v0,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) by A1644; :: thesis: verum
end;
A1648: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
Tern (v0,(Tern (v0,v1,v2)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A34;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A1646; :: thesis: verum
end;
A1651: for v104, v103, v3, v2, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,(Tern (v102,(Tern ((Tern (v102,v2,v3)),v103,v104)),v3))))) = Tern ((Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v104,(Tern ((Tern (v102,v2,v3)),v102,v103)))))
proof
let v104, v103, v3, v2, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,(Tern (v102,(Tern ((Tern (v102,v2,v3)),v103,v104)),v3))))) = Tern ((Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v104,(Tern ((Tern (v102,v2,v3)),v102,v103)))))
Tern ((Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v102,(Tern ((Tern (v102,v2,v3)),v103,v104))))) = Tern ((Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,(Tern (v102,(Tern ((Tern (v102,v2,v3)),v103,v104)),v3))))) by A419;
hence Tern ((Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,(Tern (v102,(Tern ((Tern (v102,v2,v3)),v103,v104)),v3))))) = Tern ((Tern ((Tern (v102,v2,v3)),v103,v104)),(Tern (v102,v2,v3)),(Tern ((Tern (v102,v2,v3)),v104,(Tern ((Tern (v102,v2,v3)),v102,v103))))) by A296; :: thesis: verum
end;
A1654: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
Tern ((Tern (v0,v1,v2)),v3,v4) = Tern (v4,(Tern (v0,v1,v2)),v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v4,(Tern (v0,v1,v2)),v3)),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v3,v4)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3))))) by A1651; :: thesis: verum
end;
A1657: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v4,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v4,v3)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v4,v3)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v0,v1,v2)),v0,v4)))))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v4,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v4,v3)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v4,v3)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v0,v1,v2)),v0,v4)))))
Tern (v3,(Tern (v0,v1,v2)),v4) = Tern (v4,v3,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v4,v3,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern ((Tern (v0,v1,v2)),v4,v3)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v4,v3)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v3,(Tern ((Tern (v0,v1,v2)),v0,v4))))) by A1654; :: thesis: verum
end;
A1660: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern (v4,(Tern (v0,v1,v2)),v3)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern (v4,(Tern (v0,v1,v2)),v3)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
Tern ((Tern (v0,v1,v2)),v3,v4) = Tern (v4,(Tern (v0,v1,v2)),v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern (v4,(Tern (v0,v1,v2)),v3)),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3))))) by A1657; :: thesis: verum
end;
A1662: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
Tern (v4,(Tern (v0,v1,v2)),v3) = Tern (v3,v4,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),v2))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3))))) by A1660; :: thesis: verum
end;
A1664: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),v2) = Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v1,v2))))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3))))) by A1662; :: thesis: verum
end;
A1666: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3)))))
Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A1604;
hence Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,v4)),(Tern (v0,v1,v2)),(Tern ((Tern (v0,v1,v2)),v4,(Tern ((Tern (v0,v1,v2)),v0,v3))))) by A1664; :: thesis: verum
end;
A1669: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v4,(Tern (v0,v2,v1)),v3)),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern ((Tern (v0,v2,v1)),v0,v3)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v4,(Tern (v0,v2,v1)),v3)),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern ((Tern (v0,v2,v1)),v0,v3)))))
Tern ((Tern (v0,v2,v1)),v3,v4) = Tern (v4,(Tern (v0,v2,v1)),v3) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v4,(Tern (v0,v2,v1)),v3)),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern ((Tern (v0,v2,v1)),v0,v3))))) by A1666; :: thesis: verum
end;
A1671: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern ((Tern (v0,v2,v1)),v0,v3)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern ((Tern (v0,v2,v1)),v0,v3)))))
Tern (v4,(Tern (v0,v2,v1)),v3) = Tern (v3,v4,(Tern (v0,v2,v1))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern ((Tern (v0,v2,v1)),v0,v3))))) by A1669; :: thesis: verum
end;
A1673: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern (v3,(Tern (v0,v2,v1)),v0)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern (v3,(Tern (v0,v2,v1)),v0)))))
Tern ((Tern (v0,v2,v1)),v0,v3) = Tern (v3,(Tern (v0,v2,v1)),v0) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern (v3,(Tern (v0,v2,v1)),v0))))) by A1671; :: thesis: verum
end;
A1675: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern (v0,v3,(Tern (v0,v2,v1)))))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern (v0,v3,(Tern (v0,v2,v1)))))))
Tern (v3,(Tern (v0,v2,v1)),v0) = Tern (v0,v3,(Tern (v0,v2,v1))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern ((Tern (v0,v2,v1)),v4,(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A1673; :: thesis: verum
end;
A1677: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v3,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v3,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)))))
Tern (v4,(Tern (v0,v3,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))) = Tern ((Tern (v0,v2,v1)),v4,(Tern (v0,v3,(Tern (v0,v2,v1))))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v3,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))))) by A1675; :: thesis: verum
end;
A1679: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))))
Tern (v4,(Tern (v0,v3,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1))) = Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A1677; :: thesis: verum
end;
A1681: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))),(Tern (v3,v4,(Tern (v0,v2,v1)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))),(Tern (v3,v4,(Tern (v0,v2,v1)))))
Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))),(Tern (v3,v4,(Tern (v0,v2,v1))))) = Tern ((Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))),(Tern (v3,v4,(Tern (v0,v2,v1))))) by A1679; :: thesis: verum
end;
A1683: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))))
Tern ((Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))),(Tern (v3,v4,(Tern (v0,v2,v1))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A1681; :: thesis: verum
end;
A1685: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1)))))))
Tern ((Tern (v0,v2,v1)),(Tern (v3,v4,(Tern (v0,v2,v1)))),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A1252;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v3,(Tern (v0,v2,v1)),(Tern (v4,(Tern (v0,v2,v1)),(Tern (v0,v3,(Tern (v0,v2,v1))))))) by A1683; :: thesis: verum
end;
A1689: for v1, v4, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,(Tern (v0,(Tern (v0,v2,v3)),v4))))) = Tern (v0,v3,v4)
proof
now :: thesis: for v4, v5, v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,(Tern (v0,(Tern (v0,v2,v3)),v4))))) = Tern (v0,v3,v4)
let v4, v5, v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,v4,(Tern (v0,v1,(Tern (v0,(Tern (v0,v2,v3)),v4))))) = Tern (v0,v3,v4)
Tern ((Tern (v0,v1,(Tern (v0,v2,v3)))),(Tern (v0,v3,v4)),(Tern (v4,(Tern (v0,v3,v4)),(Tern (v4,v5,(Tern (v0,v1,(Tern (v0,v2,v3))))))))) = Tern (v3,v4,(Tern (v0,v1,(Tern (v0,(Tern (v0,v2,v3)),v4))))) by A1624;
hence Tern (v3,v4,(Tern (v0,v1,(Tern (v0,(Tern (v0,v2,v3)),v4))))) = Tern (v0,v3,v4) by A1466; :: thesis: verum
end;
hence for v1, v4, v3, v2, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,(Tern (v0,(Tern (v0,v2,v3)),v4))))) = Tern (v0,v3,v4) ; :: thesis: verum
end;
A1692: for v3, v1, v0, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,(Tern (v2,v4,v0))))))) = Tern (v2,v0,v1)
proof
let v3, v1, v0, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,(Tern (v2,v4,v0))))))) = Tern (v2,v0,v1)
Tern (v2,(Tern (v2,v4,v0)),v1) = Tern (v2,v1,(Tern (v2,v4,v0))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v2,v1,(Tern (v2,v4,v0))))))) = Tern (v2,v0,v1) by A1689; :: thesis: verum
end;
A1695: for v103, v104, v101, v5, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),v101,(Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104))))) = Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),v101,(Tern (v3,v4,v5)))
proof
let v103, v104, v101, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),v101,(Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104))))) = Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),v101,(Tern (v3,v4,v5)))
Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104))))) = Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104))) by A1648;
hence Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),v101,(Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104))))) = Tern ((Tern ((Tern (v3,v4,v5)),v103,(Tern (v101,(Tern (v3,v4,v5)),v104)))),v101,(Tern (v3,v4,v5))) by A632; :: thesis: verum
end;
A1698: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,v5,(Tern (v0,v1,v2)))))),v4,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5)))),v4,(Tern (v0,v1,v2)))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,v5,(Tern (v0,v1,v2)))))),v4,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5)))),v4,(Tern (v0,v1,v2)))
Tern (v4,(Tern (v0,v1,v2)),v5) = Tern (v4,v5,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,v5,(Tern (v0,v1,v2)))))),v4,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5)))),v4,(Tern (v0,v1,v2))) by A1695; :: thesis: verum
end;
A1700: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v3,(Tern (v4,v5,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))),v4,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5)))),v4,(Tern (v0,v1,v2)))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,(Tern (v4,v5,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))),v4,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5)))),v4,(Tern (v0,v1,v2)))
Tern (v3,(Tern (v4,v5,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,v5,(Tern (v0,v1,v2))))) by A3;
hence Tern ((Tern (v3,(Tern (v4,v5,(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)))),v4,(Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5))))) = Tern ((Tern ((Tern (v0,v1,v2)),v3,(Tern (v4,(Tern (v0,v1,v2)),v5)))),v4,(Tern (v0,v1,v2))) by A1698; :: thesis: verum
end;
A1703: for v0, v1, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v3,v4,v5)),(Tern (v1,v2,(Tern (v3,v4,v5)))))),v1,(Tern ((Tern (v3,v4,v5)),v0,(Tern (v1,(Tern (v3,v4,v5)),v2))))) = Tern ((Tern ((Tern (v3,v4,v5)),v0,(Tern (v1,(Tern (v3,v4,v5)),v2)))),v1,(Tern (v3,v4,v5)))
proof
let v0, v1, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v3,v4,v5)),(Tern (v1,v2,(Tern (v3,v4,v5)))))),v1,(Tern ((Tern (v3,v4,v5)),v0,(Tern (v1,(Tern (v3,v4,v5)),v2))))) = Tern ((Tern ((Tern (v3,v4,v5)),v0,(Tern (v1,(Tern (v3,v4,v5)),v2)))),v1,(Tern (v3,v4,v5)))
Tern (v0,(Tern (v1,v2,(Tern (v3,v4,v5)))),(Tern (v3,v4,v5))) = Tern (v0,(Tern (v3,v4,v5)),(Tern (v1,v2,(Tern (v3,v4,v5))))) by A4;
hence Tern ((Tern (v0,(Tern (v3,v4,v5)),(Tern (v1,v2,(Tern (v3,v4,v5)))))),v1,(Tern ((Tern (v3,v4,v5)),v0,(Tern (v1,(Tern (v3,v4,v5)),v2))))) = Tern ((Tern ((Tern (v3,v4,v5)),v0,(Tern (v1,(Tern (v3,v4,v5)),v2)))),v1,(Tern (v3,v4,v5))) by A1700; :: thesis: verum
end;
A1706: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
Tern (v4,(Tern (v1,v2,v3)),v5) = Tern (v4,v5,(Tern (v1,v2,v3))) by A4;
hence Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3))) by A1703; :: thesis: verum
end;
A1708: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3))))) by A3;
hence Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3))) by A1706; :: thesis: verum
end;
A1710: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) by A4;
hence Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3))) by A1708; :: thesis: verum
end;
A1712: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3)))
Tern (v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) by A3;
hence Tern (v4,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,(Tern (v1,v2,v3)),v5)))),v4,(Tern (v1,v2,v3))) by A1710; :: thesis: verum
end;
A1715: for v1, v0, v5, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v5,(Tern (v2,v3,v4))))) = Tern ((Tern ((Tern (v2,v3,v4)),v1,(Tern (v0,(Tern (v2,v3,v4)),v5)))),v0,(Tern (v2,v3,v4)))
proof
let v1, v0, v5, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v5,(Tern (v2,v3,v4))))) = Tern ((Tern ((Tern (v2,v3,v4)),v1,(Tern (v0,(Tern (v2,v3,v4)),v5)))),v0,(Tern (v2,v3,v4)))
Tern (v0,(Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v5,(Tern (v2,v3,v4)))))),(Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v5,(Tern (v2,v3,v4))))))) = Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v5,(Tern (v2,v3,v4))))) by A34;
hence Tern (v1,(Tern (v2,v3,v4)),(Tern (v0,v5,(Tern (v2,v3,v4))))) = Tern ((Tern ((Tern (v2,v3,v4)),v1,(Tern (v0,(Tern (v2,v3,v4)),v5)))),v0,(Tern (v2,v3,v4))) by A1712; :: thesis: verum
end;
A1718: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3)))
Tern (v4,(Tern (v1,v2,v3)),v5) = Tern (v4,v5,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3))) by A1715; :: thesis: verum
end;
A1720: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))),v4,(Tern (v1,v2,v3)))
Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v0,(Tern (v4,v5,(Tern (v1,v2,v3))))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3)))),v4,(Tern (v1,v2,v3))) by A1718; :: thesis: verum
end;
A1722: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3)))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3)))
Tern (v0,(Tern (v4,v5,(Tern (v1,v2,v3)))),(Tern (v1,v2,v3))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3))) by A1720; :: thesis: verum
end;
A1724: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4)
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4)
Tern ((Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4,(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4) by A1722; :: thesis: verum
end;
A1726: for v0, v4, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))))
proof
let v0, v4, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))))
Tern ((Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3)))))),v4) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v5,(Tern (v1,v2,v3))))))) by A1724; :: thesis: verum
end;
A1731: for v103, v104, v102, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))) = Tern ((Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))))
proof
let v103, v104, v102, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))) = Tern ((Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))))
Tern ((Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104)))),(Tern (v3,v4,v5)),(Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))))) = Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))) by A1648;
hence Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))) = Tern ((Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104))))) by A289; :: thesis: verum
end;
A1734: for v1, v0, v5, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v5,(Tern (v2,v3,v4)),v0))) = Tern ((Tern (v0,v1,(Tern ((Tern (v2,v3,v4)),v0,v5)))),(Tern (v2,v3,v4)),(Tern ((Tern (v2,v3,v4)),v0,(Tern (v0,v1,v5)))))
proof
let v1, v0, v5, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v5,(Tern (v2,v3,v4)),v0))) = Tern ((Tern (v0,v1,(Tern ((Tern (v2,v3,v4)),v0,v5)))),(Tern (v2,v3,v4)),(Tern ((Tern (v2,v3,v4)),v0,(Tern (v0,v1,v5)))))
Tern ((Tern (v2,v3,v4)),v0,v5) = Tern (v5,(Tern (v2,v3,v4)),v0) by A3;
hence Tern (v0,v1,(Tern (v5,(Tern (v2,v3,v4)),v0))) = Tern ((Tern (v0,v1,(Tern ((Tern (v2,v3,v4)),v0,v5)))),(Tern (v2,v3,v4)),(Tern ((Tern (v2,v3,v4)),v0,(Tern (v0,v1,v5))))) by A1731; :: thesis: verum
end;
A1737: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern ((Tern (v3,v4,v5)),v0,v2)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern ((Tern (v3,v4,v5)),v0,v2)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))))
Tern (v2,(Tern (v3,v4,v5)),v0) = Tern (v0,v2,(Tern (v3,v4,v5))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern ((Tern (v3,v4,v5)),v0,v2)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))))) by A1734; :: thesis: verum
end;
A1739: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v2,(Tern (v3,v4,v5)),v0)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v2,(Tern (v3,v4,v5)),v0)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))))
Tern ((Tern (v3,v4,v5)),v0,v2) = Tern (v2,(Tern (v3,v4,v5)),v0) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v2,(Tern (v3,v4,v5)),v0)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))))) by A1737; :: thesis: verum
end;
A1741: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))))
Tern (v2,(Tern (v3,v4,v5)),v0) = Tern (v0,v2,(Tern (v3,v4,v5))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))))) by A1739; :: thesis: verum
end;
A1743: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) by A1741; :: thesis: verum
end;
A1745: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))))
Tern ((Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) by A1743; :: thesis: verum
end;
A1747: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))))
Tern ((Tern (v3,v4,v5)),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) by A1745; :: thesis: verum
end;
A1752: for v103, v104, v102, v5, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))),(Tern (v3,v4,v5)),(Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))))) = Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))
proof
let v103, v104, v102, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))),(Tern (v3,v4,v5)),(Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))))) = Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))
Tern ((Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))),(Tern (v3,v4,v5)),(Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104))))) = Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104))) by A1648;
hence Tern ((Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104)))),(Tern (v3,v4,v5)),(Tern (v102,v103,(Tern ((Tern (v3,v4,v5)),v102,v104))))) = Tern ((Tern (v3,v4,v5)),v102,(Tern (v102,v103,v104))) by A289; :: thesis: verum
end;
A1755: for v0, v1, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v3,(Tern (v3,v4,v5)),(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern ((Tern (v0,v1,v2)),v3,v5))))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5)))
proof
let v0, v1, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,(Tern (v3,v4,v5)),(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern ((Tern (v0,v1,v2)),v3,v5))))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5)))
Tern (v3,(Tern (v3,v4,v5)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5))) by A3;
hence Tern ((Tern (v3,(Tern (v3,v4,v5)),(Tern (v0,v1,v2)))),(Tern (v0,v1,v2)),(Tern (v3,v4,(Tern ((Tern (v0,v1,v2)),v3,v5))))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5))) by A1752; :: thesis: verum
end;
A1758: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v2,(Tern (v3,v4,v5)),v0))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v2,(Tern (v3,v4,v5)),v0))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
Tern ((Tern (v3,v4,v5)),v0,v2) = Tern (v2,(Tern (v3,v4,v5)),v0) by A3;
hence Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v2,(Tern (v3,v4,v5)),v0))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))) by A1755; :: thesis: verum
end;
A1760: for v3, v4, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
proof
let v3, v4, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
Tern (v2,(Tern (v3,v4,v5)),v0) = Tern (v0,v2,(Tern (v3,v4,v5))) by A3;
hence Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))) by A1758; :: thesis: verum
end;
A1762: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
Tern ((Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))))) = Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5))) by A3;
hence Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))) by A1760; :: thesis: verum
end;
A1764: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))),(Tern (v3,v4,v5))) = Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) by A3;
hence Tern ((Tern (v3,v4,v5)),(Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5)))))),(Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))) by A1762; :: thesis: verum
end;
A1767: for v4, v3, v5, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5)))
proof
let v4, v3, v5, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5)))
Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2)))))),(Tern (v3,(Tern (v3,v4,v5)),(Tern (v0,v1,v2))))) = Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2))))) by A1747;
hence Tern (v3,v4,(Tern (v3,v5,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v2)),v3,(Tern (v3,v4,v5))) by A1764; :: thesis: verum
end;
A1770: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5)))
Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))) = Tern ((Tern (v3,v4,v5)),v0,(Tern (v0,v1,v2))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern (v0,(Tern (v0,v1,v2)),(Tern (v3,v4,v5))) by A1767; :: thesis: verum
end;
A1773: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),v1))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),v1))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,v3)),v1) = Tern (v1,v0,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v2,v3)),v1))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1685; :: thesis: verum
end;
A1775: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,v3)),v1) = Tern (v0,v1,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1773; :: thesis: verum
end;
A1777: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) by A1726;
hence Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1775; :: thesis: verum
end;
A1781: for v100, v102, v101, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v101,v102)),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
proof
now :: thesis: for v100, v3, v102, v101, v4, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v101,v102)),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
let v100, v3, v102, v101, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v2,v101,v102)),(Tern (v101,v102,v100))) = Tern (v101,v102,v100)
Tern (v101,v102,(Tern (v2,v3,(Tern (v2,v102,(Tern (v2,v4,v101))))))) = Tern (v2,v101,v102) by A1692;
hence Tern (v100,(Tern (v2,v101,v102)),(Tern (v101,v102,v100))) = Tern (v101,v102,v100) by A729; :: thesis: verum
end;
hence for v100, v102, v101, v2 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v2,v101,v102)),(Tern (v101,v102,v100))) = Tern (v101,v102,v100) ; :: thesis: verum
end;
A1784: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v2,v3,v0)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v2,v3,v0)
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v2,v3,v0) by A1781; :: thesis: verum
end;
A1786: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3)
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3) by A1784; :: thesis: verum
end;
A1789: for v100, v102, v101, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v101,v102)),(Tern (v100,v103,v102))) = Tern (v100,v103,v102)
proof
now :: thesis: for v100, v102, v101, v4, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v101,v102)),(Tern (v100,v103,v102))) = Tern (v100,v103,v102)
let v100, v102, v101, v4, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v103,v101,v102)),(Tern (v100,v103,v102))) = Tern (v100,v103,v102)
Tern (v101,v102,(Tern (v103,v102,(Tern (v103,v102,(Tern (v103,v4,v101))))))) = Tern (v103,v101,v102) by A1692;
hence Tern (v100,(Tern (v103,v101,v102)),(Tern (v100,v103,v102))) = Tern (v100,v103,v102) by A1094; :: thesis: verum
end;
hence for v100, v102, v101, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v101,v102)),(Tern (v100,v103,v102))) = Tern (v100,v103,v102) ; :: thesis: verum
end;
A1793: for v100, v102, v101, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v101,v102)),(Tern (v103,v100,v101))) = Tern (v103,v100,v101)
proof
now :: thesis: for v100, v102, v101, v4, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v101,v102)),(Tern (v103,v100,v101))) = Tern (v103,v100,v101)
let v100, v102, v101, v4, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v103,v101,v102)),(Tern (v103,v100,v101))) = Tern (v103,v100,v101)
Tern (v101,v102,(Tern (v103,v101,(Tern (v103,v102,(Tern (v103,v4,v101))))))) = Tern (v103,v101,v102) by A1692;
hence Tern (v100,(Tern (v103,v101,v102)),(Tern (v103,v100,v101))) = Tern (v103,v100,v101) by A1203; :: thesis: verum
end;
hence for v100, v102, v101, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v101,v102)),(Tern (v103,v100,v101))) = Tern (v103,v100,v101) ; :: thesis: verum
end;
A1796: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v1))) = Tern (v1,v0,v2)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v1))) = Tern (v1,v0,v2)
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,v1))) = Tern (v1,v0,v2) by A1793; :: thesis: verum
end;
A1798: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v1,v0,v2)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v1,v0,v2)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v1,v0,v2) by A1796; :: thesis: verum
end;
A1800: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v2,v1)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v2,v1)
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v2,v1) by A1798; :: thesis: verum
end;
A1802: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2)
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))) = Tern (v0,v1,v2) by A1800; :: thesis: verum
end;
A1805: for v3, v103, v101, v104, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v3,v104,v101)),v101,(Tern (v102,v103,(Tern (v102,v104,v101))))) = Tern (v102,(Tern (v3,v104,v101)),v101)
proof
let v3, v103, v101, v104, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,v104,v101)),v101,(Tern (v102,v103,(Tern (v102,v104,v101))))) = Tern (v102,(Tern (v3,v104,v101)),v101)
Tern (v102,v101,(Tern (v102,v104,(Tern (v3,v104,v101))))) = Tern (v102,v104,v101) by A1370;
hence Tern ((Tern (v3,v104,v101)),v101,(Tern (v102,v103,(Tern (v102,v104,v101))))) = Tern (v102,(Tern (v3,v104,v101)),v101) by A1692; :: thesis: verum
end;
A1808: for v0, v4, v1, v3, v2 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v2,v3,v1))))) = Tern (v3,(Tern (v0,v1,v2)),v2)
proof
let v0, v4, v1, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v2,v3,v1))))) = Tern (v3,(Tern (v0,v1,v2)),v2)
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v2,v3,v1))))) = Tern (v3,(Tern (v0,v1,v2)),v2) by A1805; :: thesis: verum
end;
A1810: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v3))))) = Tern (v3,(Tern (v0,v1,v2)),v2)
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v3))))) = Tern (v3,(Tern (v0,v1,v2)),v2)
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v3))))) = Tern (v3,(Tern (v0,v1,v2)),v2) by A1808; :: thesis: verum
end;
A1812: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v0,v1,v2)),v2)
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v0,v1,v2)),v2)
Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v3))))) by A3;
hence Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v3)))),(Tern (v0,v1,v2))) = Tern (v3,(Tern (v0,v1,v2)),v2) by A1810; :: thesis: verum
end;
A1815: for v4, v2, v1, v0, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v3,v0,v1)))),(Tern (v4,v3,v0))) = Tern (v0,v1,(Tern (v4,v3,v0)))
proof
let v4, v2, v1, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v3,v0,v1)))),(Tern (v4,v3,v0))) = Tern (v0,v1,(Tern (v4,v3,v0)))
Tern (v1,(Tern (v4,v3,v0)),v0) = Tern (v0,v1,(Tern (v4,v3,v0))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v3,v0,v1)))),(Tern (v4,v3,v0))) = Tern (v0,v1,(Tern (v4,v3,v0))) by A1812; :: thesis: verum
end;
A1818: for v100, v101, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v2,v3)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100)
proof
let v100, v101, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v2,v3)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100)
Tern (v101,(Tern (v1,v2,v3)),(Tern (v101,v2,v3))) = Tern (v101,v2,v3) by A1786;
hence Tern (v100,(Tern (v101,v2,v3)),(Tern (v101,(Tern (v1,v2,v3)),v100))) = Tern (v101,(Tern (v1,v2,v3)),v100) by A729; :: thesis: verum
end;
A1821: for v0, v1, v2, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v3,v4,v2)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v0, v1, v2, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v3,v4,v2)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v3,v4,v2)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1818; :: thesis: verum
end;
A1823: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v2,v3,v4)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v2,v3,v4)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v2,v3,v4)),v0))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1821; :: thesis: verum
end;
A1825: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v4,v2,v3)),v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v4,v2,v3)),v0)
Tern (v1,(Tern (v2,v3,v4)),v0) = Tern (v0,v1,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v4,v2,v3)),v0) by A1823; :: thesis: verum
end;
A1827: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v3,v4,v2)),v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v3,v4,v2)),v0)
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v3,v4,v2)),v0) by A1825; :: thesis: verum
end;
A1829: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v2,v3,v4)),v0)
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v2,v3,v4)),v0)
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v1,(Tern (v2,v3,v4)),v0) by A1827; :: thesis: verum
end;
A1831: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v2,v3,v4)))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v2,v3,v4)))
Tern (v1,(Tern (v2,v3,v4)),v0) = Tern (v0,v1,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) = Tern (v0,v1,(Tern (v2,v3,v4))) by A1829; :: thesis: verum
end;
A1834: for v1, v102, v101, v104, v103 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v104,v101)),v101,(Tern (v102,v103,(Tern (v103,v104,v101))))) = Tern (v103,(Tern (v1,v104,v101)),v101)
proof
let v1, v102, v101, v104, v103 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v104,v101)),v101,(Tern (v102,v103,(Tern (v103,v104,v101))))) = Tern (v103,(Tern (v1,v104,v101)),v101)
Tern (v103,(Tern (v1,v104,v101)),(Tern (v103,v104,v101))) = Tern (v103,v104,v101) by A1786;
hence Tern ((Tern (v1,v104,v101)),v101,(Tern (v102,v103,(Tern (v103,v104,v101))))) = Tern (v103,(Tern (v1,v104,v101)),v101) by A1333; :: thesis: verum
end;
A1837: for v0, v3, v1, v4, v2 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v2,v4,v1))))) = Tern (v4,(Tern (v0,v1,v2)),v2)
proof
let v0, v3, v1, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v2,v4,v1))))) = Tern (v4,(Tern (v0,v1,v2)),v2)
Tern (v4,v1,v2) = Tern (v2,v4,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v2,v4,v1))))) = Tern (v4,(Tern (v0,v1,v2)),v2) by A1834; :: thesis: verum
end;
A1839: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v0,v1,v2)),v2)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v0,v1,v2)),v2)
Tern (v2,v4,v1) = Tern (v1,v2,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v0,v1,v2)),v2) by A1837; :: thesis: verum
end;
A1841: for v0, v3, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v4)))),(Tern (v0,v1,v2))) = Tern (v4,(Tern (v0,v1,v2)),v2)
proof
let v0, v3, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v4)))),(Tern (v0,v1,v2))) = Tern (v4,(Tern (v0,v1,v2)),v2)
Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v4)))),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v2)),v2,(Tern (v3,v4,(Tern (v1,v2,v4))))) by A3;
hence Tern (v2,(Tern (v3,v4,(Tern (v1,v2,v4)))),(Tern (v0,v1,v2))) = Tern (v4,(Tern (v0,v1,v2)),v2) by A1839; :: thesis: verum
end;
A1844: for v4, v1, v2, v0, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v3,v0,v2)))),(Tern (v4,v3,v0))) = Tern (v0,v2,(Tern (v4,v3,v0)))
proof
let v4, v1, v2, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v3,v0,v2)))),(Tern (v4,v3,v0))) = Tern (v0,v2,(Tern (v4,v3,v0)))
Tern (v2,(Tern (v4,v3,v0)),v0) = Tern (v0,v2,(Tern (v4,v3,v0))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v3,v0,v2)))),(Tern (v4,v3,v0))) = Tern (v0,v2,(Tern (v4,v3,v0))) by A1841; :: thesis: verum
end;
A1847: for v100, v102, v103, v2, v101 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v102,(Tern (v101,v2,v103)),(Tern (v102,v103,v103))))) = Tern (v101,v103,(Tern (v100,v101,(Tern (v102,v103,(Tern (v102,v2,v103)))))))
proof
let v100, v102, v103, v2, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v102,(Tern (v101,v2,v103)),(Tern (v102,v103,v103))))) = Tern (v101,v103,(Tern (v100,v101,(Tern (v102,v103,(Tern (v102,v2,v103)))))))
Tern (v102,(Tern (v101,v2,v103)),(Tern (v102,v103,v103))) = Tern (v102,v103,(Tern (v101,v103,(Tern (v102,v2,v103))))) by A432;
hence Tern (v100,v101,(Tern (v102,(Tern (v101,v2,v103)),(Tern (v102,v103,v103))))) = Tern (v101,v103,(Tern (v100,v101,(Tern (v102,v103,(Tern (v102,v2,v103))))))) by A236; :: thesis: verum
end;
A1850: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,(Tern (v1,v3,v4)),v4))) = Tern (v1,v4,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v4)))))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,(Tern (v1,v3,v4)),v4))) = Tern (v1,v4,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v4)))))))
Tern (v2,v4,v4) = v4 by A34;
hence Tern (v0,v1,(Tern (v2,(Tern (v1,v3,v4)),v4))) = Tern (v1,v4,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v4))))))) by A1847; :: thesis: verum
end;
A1852: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v4,(Tern (v1,v3,v4))))) = Tern (v1,v4,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v4)))))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v4,(Tern (v1,v3,v4))))) = Tern (v1,v4,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v4)))))))
Tern (v2,(Tern (v1,v3,v4)),v4) = Tern (v2,v4,(Tern (v1,v3,v4))) by A4;
hence Tern (v0,v1,(Tern (v2,v4,(Tern (v1,v3,v4))))) = Tern (v1,v4,(Tern (v0,v1,(Tern (v2,v4,(Tern (v2,v3,v4))))))) by A1850; :: thesis: verum
end;
A1855: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v3))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v4,v3)))))
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v3))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v4,v3)))))
Tern (v2,v3,(Tern (v2,v4,v3))) = Tern (v2,v4,v3) by A63;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v1,v4,v3))))) = Tern (v1,v3,(Tern (v0,v1,(Tern (v2,v4,v3))))) by A1852; :: thesis: verum
end;
A1858: for v102, v103, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v103,(Tern (v1,v2,v3)),(Tern (v102,v1,v2))))))) = Tern (v103,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v1,v2)))))
proof
let v102, v103, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v103,(Tern (v1,v2,v3)),(Tern (v102,v1,v2))))))) = Tern (v103,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v1,v2)))))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v1,v2))))) = Tern (v102,v103,(Tern (v102,v1,v2))) by A677;
hence Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v103,(Tern (v1,v2,v3)),(Tern (v102,v1,v2))))))) = Tern (v103,(Tern (v1,v2,v3)),(Tern (v102,v103,(Tern (v102,v1,v2))))) by A389; :: thesis: verum
end;
A1861: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v1,v2)))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v1,v2)))))
Tern (v0,v4,(Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v1,v2))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A1040;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v1,v2))))) by A1858; :: thesis: verum
end;
A1863: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v4,(Tern (v1,v2,v3))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v1,v2)))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v4,(Tern (v1,v2,v3))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A63;
hence Tern (v0,v4,(Tern (v1,v2,v3))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v1,v2))))) by A1861; :: thesis: verum
end;
A1869: for v101, v100, v103, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v103,(Tern (v1,v2,v3))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v100,(Tern (v1,v2,v103)),(Tern (v1,v2,v3)))))))
proof
let v101, v100, v103, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v103,(Tern (v1,v2,v3))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v100,(Tern (v1,v2,v103)),(Tern (v1,v2,v3)))))))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v100,v103,(Tern (v1,v2,v103))))) = Tern (v100,v103,(Tern (v1,v2,v3))) by A872;
hence Tern (v100,v101,(Tern (v100,v103,(Tern (v1,v2,v3))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v100,(Tern (v1,v2,v103)),(Tern (v1,v2,v3))))))) by A139; :: thesis: verum
end;
A1872: for v1, v0, v2, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v3,v4,v5)))))))
proof
let v1, v0, v2, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v3,v4,v5)))))))
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,v5))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v0,(Tern (v2,v3,v4)),(Tern (v3,v4,v5))))))) by A1869; :: thesis: verum
end;
A1876: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
Tern (v0,v4,(Tern (v1,v2,v4))) = Tern (v2,v4,(Tern (v0,v1,v4))) by A898;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A872; :: thesis: verum
end;
A1879: for v104, v100, v1, v3, v2, v101 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v1,v101,(Tern (v101,v2,v3)))),(Tern (v100,(Tern (v101,v2,v3)),v104))) = Tern (v100,v104,(Tern ((Tern (v1,v101,v2)),(Tern (v101,v2,v3)),(Tern (v100,v101,(Tern (v101,v2,v3)))))))
proof
let v104, v100, v1, v3, v2, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v1,v101,(Tern (v101,v2,v3)))),(Tern (v100,(Tern (v101,v2,v3)),v104))) = Tern (v100,v104,(Tern ((Tern (v1,v101,v2)),(Tern (v101,v2,v3)),(Tern (v100,v101,(Tern (v101,v2,v3)))))))
Tern (v101,(Tern (v1,v101,v2)),(Tern (v101,v2,v3))) = Tern (v1,v101,(Tern (v101,v2,v3))) by A517;
hence Tern (v100,(Tern (v1,v101,(Tern (v101,v2,v3)))),(Tern (v100,(Tern (v101,v2,v3)),v104))) = Tern (v100,v104,(Tern ((Tern (v1,v101,v2)),(Tern (v101,v2,v3)),(Tern (v100,v101,(Tern (v101,v2,v3))))))) by A922; :: thesis: verum
end;
A1882: for v5, v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v5,(Tern (v2,v3,v4))))) = Tern (v0,v5,(Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v2,(Tern (v2,v3,v4)))))))
proof
let v5, v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v5,(Tern (v2,v3,v4))))) = Tern (v0,v5,(Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v2,(Tern (v2,v3,v4)))))))
Tern (v0,(Tern (v2,v3,v4)),v5) = Tern (v0,v5,(Tern (v2,v3,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,v5,(Tern (v2,v3,v4))))) = Tern (v0,v5,(Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v2,(Tern (v2,v3,v4))))))) by A1879; :: thesis: verum
end;
A1887: for v103, v101, v100, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v100,(Tern (v1,v2,v3)),(Tern (v101,v100,v1)))),(Tern (v101,v103,v100))) = Tern (v100,(Tern (v1,v2,(Tern (v100,v1,v3)))),(Tern (v101,v103,v100)))
proof
let v103, v101, v100, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v100,(Tern (v1,v2,v3)),(Tern (v101,v100,v1)))),(Tern (v101,v103,v100))) = Tern (v100,(Tern (v1,v2,(Tern (v100,v1,v3)))),(Tern (v101,v103,v100)))
Tern (v100,(Tern (v1,v2,v3)),(Tern (v101,v100,v1))) = Tern (v101,v100,(Tern (v1,v2,(Tern (v100,v1,v3))))) by A948;
hence Tern (v100,(Tern (v100,(Tern (v1,v2,v3)),(Tern (v101,v100,v1)))),(Tern (v101,v103,v100))) = Tern (v100,(Tern (v1,v2,(Tern (v100,v1,v3)))),(Tern (v101,v103,v100))) by A1460; :: thesis: verum
end;
A1890: for v5, v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,v0)))),(Tern (v4,v5,v0))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
proof
let v5, v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,v0)))),(Tern (v4,v5,v0))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
Tern (v4,v0,v1) = Tern (v1,v4,v0) by A3;
hence Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,v0)))),(Tern (v4,v5,v0))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0))) by A1887; :: thesis: verum
end;
A1892: for v5, v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v4,v5,v0))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
proof
let v5, v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v4,v5,v0))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
Tern (v1,v4,v0) = Tern (v0,v1,v4) by A3;
hence Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v4,v5,v0))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0))) by A1890; :: thesis: verum
end;
A1894: for v5, v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v0,v4,v5))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
proof
let v5, v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v0,v4,v5))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
Tern (v4,v5,v0) = Tern (v0,v4,v5) by A3;
hence Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v0,v4,v5))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0))) by A1892; :: thesis: verum
end;
A1896: for v4, v5, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
proof
let v4, v5, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
Tern (v0,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4)))),(Tern (v0,v4,v5))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v0,v4,v5))))) by A1770;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0))) by A1894; :: thesis: verum
end;
A1898: for v4, v5, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v4,v5))))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
proof
let v4, v5, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v4,v5))))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
Tern (v0,(Tern (v0,v1,v4)),(Tern (v0,v4,v5))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v4,v5))))) by A1770;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v4,v5))))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0))) by A1896; :: thesis: verum
end;
A1900: for v4, v5, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
proof
let v4, v5, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0)))
Tern (v0,v4,(Tern (v0,v4,v5))) = Tern (v0,v4,v5) by A74;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v4,v5,v0))) by A1898; :: thesis: verum
end;
A1902: for v4, v5, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v0,v4,v5)))
proof
let v4, v5, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v0,v4,v5)))
Tern (v4,v5,v0) = Tern (v0,v4,v5) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v0,v4,v5))) by A1900; :: thesis: verum
end;
A1904: for v4, v5, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3)))))))
proof
let v4, v5, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,(Tern (v0,v1,v3)))),(Tern (v0,v4,v5))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3))))))) by A1076;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,v5))))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3))))))) by A1902; :: thesis: verum
end;
A1906: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3)))
Tern (v0,v4,(Tern (v2,v3,v4))) = Tern (v2,v4,(Tern (v0,v3,v4))) by A719;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A983; :: thesis: verum
end;
A1909: for v104, v102, v4, v101, v100 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,v101,(Tern (v100,(Tern (v102,(Tern (v100,v101,v4)),v104)),(Tern (v101,v102,v4))))))) = Tern (v100,v101,(Tern (v102,(Tern (v100,v101,v4)),v104)))
proof
let v104, v102, v4, v101, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,v101,(Tern (v100,(Tern (v102,(Tern (v100,v101,v4)),v104)),(Tern (v101,v102,v4))))))) = Tern (v100,v101,(Tern (v102,(Tern (v100,v101,v4)),v104)))
Tern (v100,(Tern (v102,(Tern (v100,v101,v4)),v104)),(Tern (v101,v102,(Tern (v100,v101,v4))))) = Tern (v100,v101,(Tern (v100,(Tern (v102,(Tern (v100,v101,v4)),v104)),(Tern (v101,v102,v4))))) by A103;
hence Tern (v100,v101,(Tern (v100,v101,(Tern (v100,(Tern (v102,(Tern (v100,v101,v4)),v104)),(Tern (v101,v102,v4))))))) = Tern (v100,v101,(Tern (v102,(Tern (v100,v101,v4)),v104))) by A1017; :: thesis: verum
end;
A1912: for v2, v4, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v2,v4,(Tern (v0,v1,v3)))),(Tern (v1,v2,v3))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),v4)))
proof
let v2, v4, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v2,v4,(Tern (v0,v1,v3)))),(Tern (v1,v2,v3))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),v4)))
Tern (v2,(Tern (v0,v1,v3)),v4) = Tern (v2,v4,(Tern (v0,v1,v3))) by A4;
hence Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v2,v4,(Tern (v0,v1,v3)))),(Tern (v1,v2,v3))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),v4))) by A1909; :: thesis: verum
end;
A1915: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v4)),v3)))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v4)),v3)))
Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))) = Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))) by A4;
hence Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v4)),v3))) by A1912; :: thesis: verum
end;
A1918: for v2, v4, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),v4)))
proof
let v2, v4, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),v4)))
Tern (v0,v1,(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))))) = Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) by A74;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) = Tern (v0,v1,(Tern (v2,(Tern (v0,v1,v3)),v4))) by A1915; :: thesis: verum
end;
A1920: for v2, v4, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) = Tern (v0,v1,(Tern (v2,v4,(Tern (v0,v1,v3)))))
proof
let v2, v4, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) = Tern (v0,v1,(Tern (v2,v4,(Tern (v0,v1,v3)))))
Tern (v2,(Tern (v0,v1,v3)),v4) = Tern (v2,v4,(Tern (v0,v1,v3))) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v3))))))) = Tern (v0,v1,(Tern (v2,v4,(Tern (v0,v1,v3))))) by A1918; :: thesis: verum
end;
A1923: for v103, v100, v105, v104, v101 being Element of (BA2TBAA B) holds Tern (v100,v101,(Tern (v100,(Tern (v101,v104,v105)),(Tern (v103,v104,(Tern (v100,v103,v105))))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v103,v104,v105)))))
proof
let v103, v100, v105, v104, v101 be Element of (BA2TBAA B); :: thesis: Tern (v100,v101,(Tern (v100,(Tern (v101,v104,v105)),(Tern (v103,v104,(Tern (v100,v103,v105))))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v103,v104,v105)))))
Tern (v100,v101,(Tern (v100,(Tern (v101,v104,v105)),(Tern (v103,v104,v105))))) = Tern (v100,v101,(Tern (v103,v104,v105))) by A1178;
hence Tern (v100,v101,(Tern (v100,(Tern (v101,v104,v105)),(Tern (v103,v104,(Tern (v100,v103,v105))))))) = Tern (v100,v103,(Tern (v100,v101,(Tern (v103,v104,v105))))) by A189; :: thesis: verum
end;
A1926: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,(Tern (v0,v3,v4))))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,(Tern (v0,v3,v4))))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
Tern (v0,v4,v3) = Tern (v0,v3,v4) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v4,v2,(Tern (v0,v3,v4))))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3))))) by A1923; :: thesis: verum
end;
A1928: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v3,v4)),v4))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v3,v4)),v4))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
Tern (v2,(Tern (v0,v3,v4)),v4) = Tern (v4,v2,(Tern (v0,v3,v4))) by A3;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v3,v4)),v4))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3))))) by A1926; :: thesis: verum
end;
A1930: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
Tern (v2,(Tern (v0,v3,v4)),v4) = Tern (v2,v4,(Tern (v0,v3,v4))) by A4;
hence Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3))))) by A1928; :: thesis: verum
end;
A1932: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A1906;
hence Tern (v0,v1,(Tern (v0,v4,(Tern (v1,v2,v3))))) = Tern (v0,v4,(Tern (v0,v1,(Tern (v4,v2,v3))))) by A1930; :: thesis: verum
end;
A1935: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v4,v2,v3)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v4,v2,v3)))))
Tern (v2,v3,v4) = Tern (v4,v2,v3) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v4,v2,v3))))) by A1932; :: thesis: verum
end;
A1937: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,v2)))))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,v2)))))
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,v2))))) by A1935; :: thesis: verum
end;
A1942: for v101, v103, v102, v4, v3, v2, v100 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v103,(Tern (v100,v102,(Tern (v4,v2,(Tern (v100,v2,v3))))))))) = Tern (v100,(Tern (v2,v3,(Tern (v100,v4,v2)))),(Tern (v100,v102,v103)))
proof
let v101, v103, v102, v4, v3, v2, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v103,(Tern (v100,v102,(Tern (v4,v2,(Tern (v100,v2,v3))))))))) = Tern (v100,(Tern (v2,v3,(Tern (v100,v4,v2)))),(Tern (v100,v102,v103)))
Tern (v100,v102,(Tern (v2,v3,(Tern (v100,v4,v2))))) = Tern (v100,v102,(Tern (v4,v2,(Tern (v100,v2,v3))))) by A1335;
hence Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v103,(Tern (v100,v102,(Tern (v4,v2,(Tern (v100,v2,v3))))))))) = Tern (v100,(Tern (v2,v3,(Tern (v100,v4,v2)))),(Tern (v100,v102,v103))) by A971; :: thesis: verum
end;
A1945: for v2, v3, v4, v6, v5, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v4,v5,(Tern (v0,v5,v6)))),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v5,v6,(Tern (v0,v4,v5)))),(Tern (v0,v2,v3)))
proof
now :: thesis: for v1, v3, v2, v4, v6, v5, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v4,v5,(Tern (v0,v5,v6)))),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v5,v6,(Tern (v0,v4,v5)))),(Tern (v0,v2,v3)))
let v1, v3, v2, v4, v6, v5, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v4,v5,(Tern (v0,v5,v6)))),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v5,v6,(Tern (v0,v4,v5)))),(Tern (v0,v2,v3)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v3,(Tern (v0,v2,(Tern (v4,v5,(Tern (v0,v5,v6))))))))) = Tern (v0,(Tern (v4,v5,(Tern (v0,v5,v6)))),(Tern (v0,v2,v3))) by A971;
hence Tern (v0,(Tern (v4,v5,(Tern (v0,v5,v6)))),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v5,v6,(Tern (v0,v4,v5)))),(Tern (v0,v2,v3))) by A1942; :: thesis: verum
end;
hence for v2, v3, v4, v6, v5, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v4,v5,(Tern (v0,v5,v6)))),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v5,v6,(Tern (v0,v4,v5)))),(Tern (v0,v2,v3))) ; :: thesis: verum
end;
A1948: for v4, v0, v5, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v2)))),(Tern (v0,v4,v5)))
proof
let v4, v0, v5, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v2)))),(Tern (v0,v4,v5)))
Tern (v0,(Tern (v1,v2,(Tern (v0,v2,v3)))),(Tern (v0,v4,v5))) = Tern (v0,v2,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3))))))) by A1097;
hence Tern (v0,v2,(Tern (v0,v4,(Tern (v0,v5,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v2)))),(Tern (v0,v4,v5))) by A1945; :: thesis: verum
end;
A1954: for v102, v103, v101, v100, v1 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,(Tern (v1,v100,v101)),(Tern (v102,v103,(Tern (v1,v100,v101))))))) = Tern (v1,v100,(Tern (v101,v102,(Tern (v100,v101,v103)))))
proof
let v102, v103, v101, v100, v1 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,(Tern (v1,v100,v101)),(Tern (v102,v103,(Tern (v1,v100,v101))))))) = Tern (v1,v100,(Tern (v101,v102,(Tern (v100,v101,v103)))))
Tern (v100,(Tern (v1,v100,v101)),(Tern (v101,v102,v103))) = Tern (v1,v100,(Tern (v101,v102,(Tern (v100,v101,v103))))) by A1565;
hence Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,(Tern (v1,v100,v101)),(Tern (v102,v103,(Tern (v1,v100,v101))))))) = Tern (v1,v100,(Tern (v101,v102,(Tern (v100,v101,v103))))) by A983; :: thesis: verum
end;
A1957: for v2, v3, v1, v0, v4 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v4,v0)),(Tern (v2,v3,(Tern (v4,v0,v1))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v1, v0, v4 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v4,v0)),(Tern (v2,v3,(Tern (v4,v0,v1))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v4,v0,v1) = Tern (v1,v4,v0) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v1,v4,v0)),(Tern (v2,v3,(Tern (v4,v0,v1))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A1954; :: thesis: verum
end;
A1959: for v2, v3, v1, v0, v4 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v4,v0,v1))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v1, v0, v4 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v4,v0,v1))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v1,v4,v0) = Tern (v0,v1,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v4,v0,v1))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A1957; :: thesis: verum
end;
A1961: for v2, v3, v0, v4, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v1,v4,v0))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v0, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v1,v4,v0))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v4,v0,v1) = Tern (v1,v4,v0) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v1,v4,v0))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A1959; :: thesis: verum
end;
A1963: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v1,v4,v0) = Tern (v0,v1,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A1961; :: thesis: verum
end;
A1965: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v0,(Tern (v0,v1,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v4))))))) by A1770;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A1963; :: thesis: verum
end;
A1967: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v4,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v4,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,v4,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,v1,(Tern (v0,v4,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))))) by A1904;
hence Tern (v0,v1,(Tern (v0,v4,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))))) = Tern (v4,v0,(Tern (v1,v2,(Tern (v0,v1,v3))))) by A1965; :: thesis: verum
end;
A1970: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern (v2,v0,(Tern (v1,v3,(Tern (v0,v1,v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern (v2,v0,(Tern (v1,v3,(Tern (v0,v1,v4)))))
Tern (v0,(Tern (v3,v4,(Tern (v0,v1,v2)))),(Tern (v1,v3,v4))) = Tern (v0,(Tern (v1,v3,v4)),(Tern (v3,v4,(Tern (v0,v1,v2))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern (v2,v0,(Tern (v1,v3,(Tern (v0,v1,v4))))) by A1967; :: thesis: verum
end;
A1972: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,(Tern (v1,v3,(Tern (v0,v1,v4)))))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,(Tern (v1,v3,(Tern (v0,v1,v4)))))
Tern (v0,v1,(Tern (v0,v2,(Tern (v0,(Tern (v1,v3,v4)),(Tern (v3,v4,(Tern (v0,v1,v2))))))))) = Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) by A1872;
hence Tern (v0,v2,(Tern (v0,v1,(Tern (v3,v4,(Tern (v0,v1,v2))))))) = Tern (v2,v0,(Tern (v1,v3,(Tern (v0,v1,v4))))) by A1970; :: thesis: verum
end;
A1975: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1)
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1)
Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1) = Tern (v1,v0,(Tern (v2,v3,(Tern (v0,v2,v4))))) by A3;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1) by A1972; :: thesis: verum
end;
A1977: for v3, v4, v1, v2, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))
proof
let v3, v4, v1, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4)))))
Tern (v0,(Tern (v2,v3,(Tern (v0,v2,v4)))),v1) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) by A4;
hence Tern (v0,v1,(Tern (v0,v2,(Tern (v3,v4,(Tern (v0,v2,v1))))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v2,v4))))) by A1975; :: thesis: verum
end;
A1979: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v4))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v4,v0,(Tern (v1,v2,v3)))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v4))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v4,v0,(Tern (v1,v2,v3)))))))
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v4,v1,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,(Tern (v1,v2,v3)),v4))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v4,v0,(Tern (v1,v2,v3))))))) by A1777; :: thesis: verum
end;
A1981: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v4,v0,(Tern (v1,v2,v3)))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v4,v0,(Tern (v1,v2,v3)))))))
Tern (v1,(Tern (v1,v2,v3)),v4) = Tern (v1,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v4,v0,(Tern (v1,v2,v3))))))) by A1979; :: thesis: verum
end;
A1983: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v4)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v4)))))
Tern (v0,(Tern (v1,v2,v3)),v4) = Tern (v4,v0,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v4))))) by A1981; :: thesis: verum
end;
A1985: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,v3)),v4) = Tern (v0,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1983; :: thesis: verum
end;
A1987: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4)))))
Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))) by A1977;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))) by A1985; :: thesis: verum
end;
A1989: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2)))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v2,v0,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))) by A1987; :: thesis: verum
end;
A1991: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4)))))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v0,v2,(Tern (v1,v2,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) by A1989; :: thesis: verum
end;
A1993: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))) by A1977;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1553; :: thesis: verum
end;
A1995: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v2,v0,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1993; :: thesis: verum
end;
A1997: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3)))))))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v0,v2,(Tern (v1,v2,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) by A1995; :: thesis: verum
end;
A1999: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4)))))
Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))) by A1977;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))) by A1997; :: thesis: verum
end;
A2001: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2)))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2)))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v2,v0,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))) by A1999; :: thesis: verum
end;
A2003: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4)))))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v0,v2,(Tern (v1,v2,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) by A2001; :: thesis: verum
end;
A2005: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),v4) = Tern (v4,v0,(Tern (v1,v2,v3))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,(Tern (v1,v2,v3)),v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3))))) by A1510; :: thesis: verum
end;
A2007: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),v4) = Tern (v0,v4,(Tern (v1,v2,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3))))) by A2005; :: thesis: verum
end;
A2009: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
Tern (v1,v3,(Tern (v1,v2,(Tern (v0,v4,(Tern (v1,v2,v3))))))) = Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))) by A1977;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v2,v0,(Tern (v1,v2,v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3))))) by A2007; :: thesis: verum
end;
A2011: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v2,v0,(Tern (v1,v2,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,(Tern (v1,v2,v4)),v2))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3))))) by A2009; :: thesis: verum
end;
A2013: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v4)),v2) = Tern (v0,v2,(Tern (v1,v2,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3))))) by A2011; :: thesis: verum
end;
A2015: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) by A2003;
hence Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v0,(Tern (v1,v2,v3))))) by A2013; :: thesis: verum
end;
A2018: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v4,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v0,v3,v1)),v0)))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v4,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v0,v3,v1)),v0)))
Tern (v2,(Tern (v0,v3,v1)),v0) = Tern (v0,v2,(Tern (v0,v3,v1))) by A3;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v4,(Tern (v0,v3,v1)),(Tern (v2,(Tern (v0,v3,v1)),v0))) by A2015; :: thesis: verum
end;
A2020: for v1, v2, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v4,(Tern (v0,v3,v1)),(Tern (v2,v0,(Tern (v0,v3,v1)))))
proof
let v1, v2, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v4,(Tern (v0,v3,v1)),(Tern (v2,v0,(Tern (v0,v3,v1)))))
Tern (v2,(Tern (v0,v3,v1)),v0) = Tern (v2,v0,(Tern (v0,v3,v1))) by A4;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v3,v4))))) = Tern (v4,(Tern (v0,v3,v1)),(Tern (v2,v0,(Tern (v0,v3,v1))))) by A2018; :: thesis: verum
end;
A2024: for v3, v0, v4, v2, v1 being Element of (BA2TBAA B) holds Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2)))))
proof
let v3, v0, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v4,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) by A1991;
hence Tern (v1,v3,(Tern (v0,v2,(Tern (v1,v2,v4))))) = Tern (v4,(Tern (v1,v2,v3)),(Tern (v1,v3,(Tern (v0,v1,v2))))) by A763; :: thesis: verum
end;
A2029: for v1, v5, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v3,v5,(Tern (v0,v4,(Tern (v3,v4,(Tern (v2,v3,v4))))))))) = Tern (v0,(Tern (v2,v3,(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v3,v4,v5)))))
proof
let v1, v5, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v3,v5,(Tern (v0,v4,(Tern (v3,v4,(Tern (v2,v3,v4))))))))) = Tern (v0,(Tern (v2,v3,(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v3,v4,v5)))))
Tern ((Tern (v2,v3,v4)),(Tern (v3,v4,v5)),(Tern (v0,v3,(Tern (v3,v4,v5))))) = Tern (v3,v5,(Tern (v0,v4,(Tern (v3,v4,(Tern (v2,v3,v4))))))) by A2020;
hence Tern (v0,v1,(Tern (v3,v5,(Tern (v0,v4,(Tern (v3,v4,(Tern (v2,v3,v4))))))))) = Tern (v0,(Tern (v2,v3,(Tern (v3,v4,v5)))),(Tern (v0,v1,(Tern (v3,v4,v5))))) by A1882; :: thesis: verum
end;
A2032: for v1, v3, v0, v4, v2, v5 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v4,(Tern (v5,v2,v4))))))) = Tern (v0,(Tern (v5,v2,(Tern (v2,v4,v3)))),(Tern (v0,v1,(Tern (v2,v4,v3)))))
proof
let v1, v3, v0, v4, v2, v5 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v4,(Tern (v5,v2,v4))))))) = Tern (v0,(Tern (v5,v2,(Tern (v2,v4,v3)))),(Tern (v0,v1,(Tern (v2,v4,v3)))))
Tern (v2,v4,(Tern (v5,v2,v4))) = Tern (v5,v2,v4) by A366;
hence Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v4,(Tern (v5,v2,v4))))))) = Tern (v0,(Tern (v5,v2,(Tern (v2,v4,v3)))),(Tern (v0,v1,(Tern (v2,v4,v3))))) by A2029; :: thesis: verum
end;
A2036: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v4)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v4)))
Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v4)))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v4))))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,(Tern (v1,v2,v3))))))) by A2032;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,v4))) by A974; :: thesis: verum
end;
A2039: for v101, v102, v2, v1, v100, v103 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,(Tern (v1,v2,(Tern (v103,v100,v1)))),(Tern (v102,v103,v100))))) = Tern (v100,v1,(Tern (v102,v103,v100)))
proof
let v101, v102, v2, v1, v100, v103 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,(Tern (v1,v2,(Tern (v103,v100,v1)))),(Tern (v102,v103,v100))))) = Tern (v100,v1,(Tern (v102,v103,v100)))
Tern (v100,(Tern (v1,v2,(Tern (v103,v100,v1)))),(Tern (v102,v103,v100))) = Tern (v100,v1,(Tern (v102,v103,v100))) by A1815;
hence Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,(Tern (v1,v2,(Tern (v103,v100,v1)))),(Tern (v102,v103,v100))))) = Tern (v100,v1,(Tern (v102,v103,v100))) by A1397; :: thesis: verum
end;
A2042: for v1, v2, v5, v3, v4, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v4,v3)))),(Tern (v2,v3,v0))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
proof
let v1, v2, v5, v3, v4, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v4,v3)))),(Tern (v2,v3,v0))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
Tern (v0,v4,v3) = Tern (v3,v0,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v4,v3)))),(Tern (v2,v3,v0))))) = Tern (v0,v4,(Tern (v2,v3,v0))) by A2039; :: thesis: verum
end;
A2044: for v1, v2, v5, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v2,v3,v0))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
proof
let v1, v2, v5, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v2,v3,v0))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
Tern (v0,v4,v3) = Tern (v0,v3,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v2,v3,v0))))) = Tern (v0,v4,(Tern (v2,v3,v0))) by A2042; :: thesis: verum
end;
A2046: for v1, v2, v5, v4, v3, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v0,v2,v3))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
proof
let v1, v2, v5, v4, v3, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v0,v2,v3))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v0,v2,v3))))) = Tern (v0,v4,(Tern (v2,v3,v0))) by A2044; :: thesis: verum
end;
A2048: for v1, v2, v0, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v2,(Tern (v0,v3,(Tern (v3,v4,v5))))))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
proof
let v1, v2, v0, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v2,(Tern (v0,v3,(Tern (v3,v4,v5))))))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
Tern (v0,(Tern (v4,v5,(Tern (v0,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v4,(Tern (v0,v2,(Tern (v0,v3,(Tern (v3,v4,v5))))))) by A1948;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v4,(Tern (v0,v2,(Tern (v0,v3,(Tern (v3,v4,v5))))))))) = Tern (v0,v4,(Tern (v2,v3,v0))) by A2046; :: thesis: verum
end;
A2050: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
proof
now :: thesis: for v1, v2, v0, v5, v4, v3 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
let v1, v2, v0, v5, v4, v3 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v2,v3,v0)))
Tern (v0,v4,(Tern (v0,v2,(Tern (v0,v3,(Tern (v3,v4,v5))))))) = Tern (v0,v2,(Tern (v0,v3,v4))) by A619;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v2,v3,v0))) by A2048; :: thesis: verum
end;
hence for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v2,v3,v0))) ; :: thesis: verum
end;
A2052: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v0,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v0,v2,v3)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,v4))))) = Tern (v0,v4,(Tern (v0,v2,v3))) by A2050; :: thesis: verum
end;
A2055: for v4, v1, v2, v102, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,(Tern (v3,v102,v2)))),(Tern (v4,v3,v102)),v102) = Tern (v102,v2,(Tern (v4,v3,v102)))
proof
let v4, v1, v2, v102, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,(Tern (v3,v102,v2)))),(Tern (v4,v3,v102)),v102) = Tern (v102,v2,(Tern (v4,v3,v102)))
Tern (v102,(Tern (v1,v2,(Tern (v3,v102,v2)))),(Tern (v4,v3,v102))) = Tern (v102,v2,(Tern (v4,v3,v102))) by A1844;
hence Tern ((Tern (v1,v2,(Tern (v3,v102,v2)))),(Tern (v4,v3,v102)),v102) = Tern (v102,v2,(Tern (v4,v3,v102))) by A3; :: thesis: verum
end;
A2058: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v4,v2,v3)),v3) = Tern (v3,v1,(Tern (v4,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v4,v2,v3)),v3) = Tern (v3,v1,(Tern (v4,v2,v3)))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v4,v2,v3)),v3) = Tern (v3,v1,(Tern (v4,v2,v3))) by A2055; :: thesis: verum
end;
A2060: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,v4,v2)),v3) = Tern (v3,v1,(Tern (v4,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,v4,v2)),v3) = Tern (v3,v1,(Tern (v4,v2,v3)))
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,v4,v2)),v3) = Tern (v3,v1,(Tern (v4,v2,v3))) by A2058; :: thesis: verum
end;
A2062: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4)),v3) = Tern (v3,v1,(Tern (v4,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4)),v3) = Tern (v3,v1,(Tern (v4,v2,v3)))
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4)),v3) = Tern (v3,v1,(Tern (v4,v2,v3))) by A2060; :: thesis: verum
end;
A2064: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4))) = Tern (v3,v1,(Tern (v4,v2,v3)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4))) = Tern (v3,v1,(Tern (v4,v2,v3)))
Tern ((Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4)),v3) = Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4))) by A3;
hence Tern (v3,(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v2,v3,v4))) = Tern (v3,v1,(Tern (v4,v2,v3))) by A2062; :: thesis: verum
end;
A2067: for v4, v1, v0, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v0,v2,(Tern (v0,v4,v3)))
proof
let v4, v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v0,v2,(Tern (v0,v4,v3)))
Tern (v4,v3,v0) = Tern (v0,v4,v3) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v0,v2,(Tern (v0,v4,v3))) by A2064; :: thesis: verum
end;
A2069: for v4, v1, v0, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v0,v2,(Tern (v3,v0,v4)))
proof
let v4, v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v0,v2,(Tern (v3,v0,v4)))
Tern (v0,v4,v3) = Tern (v3,v0,v4) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v0,v2,(Tern (v3,v0,v4))) by A2067; :: thesis: verum
end;
A2071: for v4, v1, v0, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v2,(Tern (v3,v0,v4)),v0)
proof
let v4, v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v2,(Tern (v3,v0,v4)),v0)
Tern (v2,(Tern (v3,v0,v4)),v0) = Tern (v0,v2,(Tern (v3,v0,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v2,(Tern (v3,v0,v4)),v0) by A2069; :: thesis: verum
end;
A2073: for v4, v1, v0, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v2,v0,(Tern (v3,v0,v4)))
proof
let v4, v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v2,v0,(Tern (v3,v0,v4)))
Tern (v2,(Tern (v3,v0,v4)),v0) = Tern (v2,v0,(Tern (v3,v0,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,v0)))),(Tern (v3,v0,v4))) = Tern (v2,v0,(Tern (v3,v0,v4))) by A2071; :: thesis: verum
end;
A2076: for v104, v102, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v102,(Tern (v104,v2,v3)),(Tern (v102,(Tern (v2,v3,v4)),(Tern ((Tern (v104,v2,v3)),v104,(Tern (v2,v3,v4))))))) = Tern ((Tern (v104,v2,v3)),(Tern (v2,v3,v4)),(Tern (v102,v104,(Tern (v2,v3,v4)))))
proof
let v104, v102, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v102,(Tern (v104,v2,v3)),(Tern (v102,(Tern (v2,v3,v4)),(Tern ((Tern (v104,v2,v3)),v104,(Tern (v2,v3,v4))))))) = Tern ((Tern (v104,v2,v3)),(Tern (v2,v3,v4)),(Tern (v102,v104,(Tern (v2,v3,v4)))))
Tern (v102,(Tern (v104,v2,v3)),(Tern (v102,v104,(Tern (v2,v3,v4))))) = Tern (v102,v104,(Tern (v2,v3,v4))) by A1831;
hence Tern (v102,(Tern (v104,v2,v3)),(Tern (v102,(Tern (v2,v3,v4)),(Tern ((Tern (v104,v2,v3)),v104,(Tern (v2,v3,v4))))))) = Tern ((Tern (v104,v2,v3)),(Tern (v2,v3,v4)),(Tern (v102,v104,(Tern (v2,v3,v4))))) by A1855; :: thesis: verum
end;
A2079: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),v1,(Tern (v2,v3,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4))))) by A2076; :: thesis: verum
end;
A2081: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v1,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))) = Tern (v1,v2,v3) by A1802;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4))))) by A2079; :: thesis: verum
end;
A2083: for v1, v0, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v1, v0, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))) by A63;
hence Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v2,v3))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,(Tern (v2,v3,v4))))) by A2081; :: thesis: verum
end;
A2089: for v104, v103, v102, v101, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v101,v102)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v1,v101,v102)),(Tern (v101,v102,v103)))
proof
let v104, v103, v102, v101, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v101,v102)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v1,v101,v102)),(Tern (v101,v102,v103)))
Tern (v104,(Tern (v1,v101,v102)),(Tern (v104,v101,v102))) = Tern (v104,v101,v102) by A1786;
hence Tern ((Tern (v1,v101,v102)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v1,v101,v102)),(Tern (v101,v102,v103))) by A1863; :: thesis: verum
end;
A2092: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v2,v4,v1))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v1,v2,v3)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v2,v4,v1))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v1,v2,v3)))
Tern (v4,v1,v2) = Tern (v2,v4,v1) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v2,v4,v1))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) by A2089; :: thesis: verum
end;
A2094: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v1,v2,v3)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v1,v2,v3)))
Tern (v2,v4,v1) = Tern (v1,v2,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) by A2092; :: thesis: verum
end;
A2097: for v104, v103, v102, v2, v101 being Element of (BA2TBAA B) holds Tern ((Tern (v101,v2,v102)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v101,v2,v102)),(Tern (v101,v102,v103)))
proof
let v104, v103, v102, v2, v101 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v101,v2,v102)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v101,v2,v102)),(Tern (v101,v102,v103)))
Tern (v104,(Tern (v101,v2,v102)),(Tern (v104,v101,v102))) = Tern (v104,v101,v102) by A1789;
hence Tern ((Tern (v101,v2,v102)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v101,v2,v102)),(Tern (v101,v102,v103))) by A1863; :: thesis: verum
end;
A2100: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v2,v4,v0))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v2,v3)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v2,v4,v0))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v2,v3)))
Tern (v4,v0,v2) = Tern (v2,v4,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v2,v4,v0))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) by A2097; :: thesis: verum
end;
A2102: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v2,v3)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v2,v3)))
Tern (v2,v4,v0) = Tern (v0,v2,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) by A2100; :: thesis: verum
end;
A2105: for v104, v103, v3, v102, v101 being Element of (BA2TBAA B) holds Tern ((Tern (v101,v102,v3)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v101,v102,v3)),(Tern (v101,v102,v103)))
proof
let v104, v103, v3, v102, v101 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v101,v102,v3)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v101,v102,v3)),(Tern (v101,v102,v103)))
Tern (v104,(Tern (v101,v102,v3)),(Tern (v104,v101,v102))) = Tern (v104,v101,v102) by A1802;
hence Tern ((Tern (v101,v102,v3)),(Tern (v101,v102,v103)),(Tern (v104,v101,v102))) = Tern (v104,(Tern (v101,v102,v3)),(Tern (v101,v102,v103))) by A1863; :: thesis: verum
end;
A2108: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v1,v4,v0))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v1,v4,v0))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))
Tern (v4,v0,v1) = Tern (v1,v4,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v1,v4,v0))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) by A2105; :: thesis: verum
end;
A2110: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))
Tern (v1,v4,v0) = Tern (v0,v1,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,v4))) = Tern (v4,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) by A2108; :: thesis: verum
end;
A2113: for v101, v104, v3, v102 being Element of (BA2TBAA B) holds Tern ((Tern (v101,v102,v3)),(Tern (v101,v102,(Tern (v102,v3,v104)))),(Tern (v104,(Tern (v101,v102,v3)),(Tern (v104,v101,v102))))) = Tern (v102,v104,(Tern (v101,v102,v3)))
proof
let v101, v104, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v101,v102,v3)),(Tern (v101,v102,(Tern (v102,v3,v104)))),(Tern (v104,(Tern (v101,v102,v3)),(Tern (v104,v101,v102))))) = Tern (v102,v104,(Tern (v101,v102,v3)))
Tern (v104,(Tern (v101,v102,v3)),(Tern (v101,v102,(Tern (v102,v3,v104))))) = Tern (v102,v104,(Tern (v101,v102,v3))) by A1073;
hence Tern ((Tern (v101,v102,v3)),(Tern (v101,v102,(Tern (v102,v3,v104)))),(Tern (v104,(Tern (v101,v102,v3)),(Tern (v104,v101,v102))))) = Tern (v102,v104,(Tern (v101,v102,v3))) by A1863; :: thesis: verum
end;
A2116: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v3,v0))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v3,v0))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v3,v0,v1) = Tern (v1,v3,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v1,v3,v0))))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A2113; :: thesis: verum
end;
A2118: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v1,v3,v0) = Tern (v0,v1,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A2116; :: thesis: verum
end;
A2120: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern (v0,v1,v3) by A729;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A2118; :: thesis: verum
end;
A2122: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,(Tern (v1,v2,v3)))),(Tern (v0,v1,v3))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A2120; :: thesis: verum
end;
A2124: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
proof
let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v1,v2,v3))))) = Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) by A2110;
hence Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern (v1,v3,(Tern (v0,v1,v2))) by A2122; :: thesis: verum
end;
A2128: for v2, v1, v0, v3 being Element of (BA2TBAA B) holds Tern ((Tern (v3,v0,v1)),(Tern (v3,v0,v2)),(Tern (v0,v1,v2))) = Tern (v0,v2,(Tern (v3,v0,v1)))
proof
let v2, v1, v0, v3 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v3,v0,v1)),(Tern (v3,v0,v2)),(Tern (v0,v1,v2))) = Tern (v0,v2,(Tern (v3,v0,v1)))
Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v1)),(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v3,v0,v1))) by A2124;
hence Tern ((Tern (v3,v0,v1)),(Tern (v3,v0,v2)),(Tern (v0,v1,v2))) = Tern (v0,v2,(Tern (v3,v0,v1))) by A3; :: thesis: verum
end;
A2131: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v0)),(Tern (v3,v0,v1)),(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v3,v0,v1)))
proof
let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v0)),(Tern (v3,v0,v1)),(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v3,v0,v1)))
Tern (v1,v2,v0) = Tern (v0,v1,v2) by A3;
hence Tern ((Tern (v1,v2,v0)),(Tern (v3,v0,v1)),(Tern (v3,v0,v2))) = Tern (v0,v2,(Tern (v3,v0,v1))) by A2124; :: thesis: verum
end;
A2134: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v2)),(Tern (v3,v2,v1))) = Tern (v2,v1,(Tern (v3,v2,v0)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v2)),(Tern (v3,v2,v1))) = Tern (v2,v1,(Tern (v3,v2,v0)))
Tern (v3,v2,v0) = Tern (v0,v3,v2) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v2)),(Tern (v3,v2,v1))) = Tern (v2,v1,(Tern (v3,v2,v0))) by A2131; :: thesis: verum
end;
A2136: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v3,v2,v1))) = Tern (v2,v1,(Tern (v3,v2,v0)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v3,v2,v1))) = Tern (v2,v1,(Tern (v3,v2,v0)))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v3,v2,v1))) = Tern (v2,v1,(Tern (v3,v2,v0))) by A2134; :: thesis: verum
end;
A2138: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v3,v2))) = Tern (v2,v1,(Tern (v3,v2,v0)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v3,v2))) = Tern (v2,v1,(Tern (v3,v2,v0)))
Tern (v3,v2,v1) = Tern (v1,v3,v2) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v3,v2))) = Tern (v2,v1,(Tern (v3,v2,v0))) by A2136; :: thesis: verum
end;
A2140: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v3,v2,v0)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v3,v2,v0)))
Tern (v1,v3,v2) = Tern (v1,v2,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v3,v2,v0))) by A2138; :: thesis: verum
end;
A2142: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v3,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v3,v2)))
Tern (v3,v2,v0) = Tern (v0,v3,v2) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v3,v2))) by A2140; :: thesis: verum
end;
A2144: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v2,v3)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v2,v3)))
Tern (v0,v3,v2) = Tern (v0,v2,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v2,v1,(Tern (v0,v2,v3))) by A2142; :: thesis: verum
end;
A2146: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v2,v3)),v2)
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v2,v3)),v2)
Tern (v1,(Tern (v0,v2,v3)),v2) = Tern (v2,v1,(Tern (v0,v2,v3))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,(Tern (v0,v2,v3)),v2) by A2144; :: thesis: verum
end;
A2148: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v2,v3)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v2,v3)))
Tern (v1,(Tern (v0,v2,v3)),v2) = Tern (v1,v2,(Tern (v0,v2,v3))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v2,v3))) by A2146; :: thesis: verum
end;
A2151: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) = Tern (v1,v2,(Tern (v0,v2,v3))) by A2148;
hence Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) by A63; :: thesis: verum
end;
A2153: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v2,v3)),(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3)))
proof
let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v2,v3)),(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3)))
Tern ((Tern (v0,v1,v2)),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v2,v3))))) = Tern ((Tern (v0,v2,v3)),(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) by A2094;
hence Tern ((Tern (v0,v2,v3)),(Tern (v0,v1,v2)),(Tern (v1,v2,v3))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v1,v2,v3))) by A2151; :: thesis: verum
end;
A2156: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v1)),(Tern (v3,v1,v2))) = Tern (v3,v1,(Tern (v0,v1,v2)))
proof
let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v1)),(Tern (v3,v1,v2))) = Tern (v3,v1,(Tern (v0,v1,v2)))
Tern ((Tern (v0,v3,v1)),(Tern (v0,v1,v2)),(Tern (v3,v1,v2))) = Tern (v3,v1,(Tern (v0,v1,v2))) by A2148;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v1)),(Tern (v3,v1,v2))) = Tern (v3,v1,(Tern (v0,v1,v2))) by A2153; :: thesis: verum
end;
A2159: for v0, v104, v105, v103, v100 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v103,v104,(Tern (v0,v104,(Tern (v100,v103,v105)))))),(Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v100,v103,(Tern (v100,(Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v103,v104,v105))))))))) = Tern (v100,(Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v103,v104,(Tern (v100,v103,v105)))))))
proof
let v0, v104, v105, v103, v100 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v103,v104,(Tern (v0,v104,(Tern (v100,v103,v105)))))),(Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v100,v103,(Tern (v100,(Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v103,v104,v105))))))))) = Tern (v100,(Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v103,v104,(Tern (v100,v103,v105)))))))
Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v103,v104,(Tern (v100,v103,v105))))) = Tern (v103,v104,(Tern (v0,v104,(Tern (v100,v103,v105))))) by A2156;
hence Tern (v100,(Tern (v103,v104,(Tern (v0,v104,(Tern (v100,v103,v105)))))),(Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v100,v103,(Tern (v100,(Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v103,v104,v105))))))))) = Tern (v100,(Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern ((Tern (v0,v104,(Tern (v100,v103,v105)))),(Tern (v0,v103,v104)),(Tern (v103,v104,(Tern (v100,v103,v105))))))) by A355; :: thesis: verum
end;
A2162: for v3, v2, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,(Tern (v0,v1,v4)),v3)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v3, v2, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,(Tern (v0,v1,v4)),v3)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v3,v2,(Tern (v0,v1,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,(Tern (v0,v1,v4)),v3)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2159; :: thesis: verum
end;
A2165: for v2, v4, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v4,(Tern (v0,v1,v3)))))),(Tern ((Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v4,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v1,v2,v3))))))))) = Tern (v0,(Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern ((Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v4,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v3)))))))
proof
let v2, v4, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v4,(Tern (v0,v1,v3)))))),(Tern ((Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v4,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v1,v2,v3))))))))) = Tern (v0,(Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern ((Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v4,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v3)))))))
Tern (v2,(Tern (v0,v1,v3)),v4) = Tern (v2,v4,(Tern (v0,v1,v3))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v4,(Tern (v0,v1,v3)))))),(Tern ((Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v4,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v1,v2,v3))))))))) = Tern (v0,(Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern ((Tern (v4,v2,(Tern (v0,v1,v3)))),(Tern (v4,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v3))))))) by A2162; :: thesis: verum
end;
A2168: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v3,v2,(Tern (v0,v1,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2165; :: thesis: verum
end;
A2170: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v2,v3,(Tern (v0,v1,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2168; :: thesis: verum
end;
A2172: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,v3,v1)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,v3,v1)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,v3,v1)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2170; :: thesis: verum
end;
A2174: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2172; :: thesis: verum
end;
A2176: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v3,v2,(Tern (v0,v1,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2174; :: thesis: verum
end;
A2178: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v2,v3,(Tern (v0,v1,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2176; :: thesis: verum
end;
A2180: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v4))) = Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2178; :: thesis: verum
end;
A2182: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v0,v1,(Tern (v0,(Tern (v1,v2,v4)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))) by A1920;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2180; :: thesis: verum
end;
A2184: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))) by A3;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2182; :: thesis: verum
end;
A2186: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern ((Tern (v1,v2,v3)),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2184; :: thesis: verum
end;
A2188: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern ((Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v0,v1,(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))) by A2083;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2186; :: thesis: verum
end;
A2190: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) by A4;
hence Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2188; :: thesis: verum
end;
A2192: for v3, v2, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v3, v2, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v0,(Tern (v1,v2,(Tern (v2,v3,(Tern (v0,v1,v4)))))),(Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v1,v2,v3))))))) by A2032;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2190; :: thesis: verum
end;
A2194: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v0,v3,(Tern (v1,v2,v3))))))) = Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) by A2036;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2192; :: thesis: verum
end;
A2196: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v3,v2,(Tern (v0,v1,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2194; :: thesis: verum
end;
A2198: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v2,v3,(Tern (v0,v1,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v3,v2,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2196; :: thesis: verum
end;
A2200: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v3,v2,(Tern (v0,v1,v4))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,(Tern (v0,v1,v4)),v3)),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2198; :: thesis: verum
end;
A2202: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,(Tern (v0,v1,v4)),v3) = Tern (v2,v3,(Tern (v0,v1,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v3,v1,v2)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2200; :: thesis: verum
end;
A2204: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,v3,v1)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,v3,v1)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v3,v1,v2) = Tern (v2,v3,v1) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,v3,v1)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2202; :: thesis: verum
end;
A2206: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))))))
Tern (v2,v3,v1) = Tern (v1,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4))))))) by A2204; :: thesis: verum
end;
A2208: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))),(Tern (v2,v3,(Tern (v0,v1,v4)))))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))),(Tern (v2,v3,(Tern (v0,v1,v4)))))))
Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern ((Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4))))) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))),(Tern (v2,v3,(Tern (v0,v1,v4))))))) by A2206; :: thesis: verum
end;
A2210: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v2,v3)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v2,v3)))))
Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,(Tern (v0,v1,v4)))),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v2,v3))) by A2128;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v2,v3))))) by A2208; :: thesis: verum
end;
A2212: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v2,v3,v0)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v2,v3,v0)))))
Tern (v0,(Tern (v2,v3,(Tern (v0,v1,v4)))),(Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v2,v3))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v2,v3,v0))))) by A2024;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v2,v3,v0))))) by A2210; :: thesis: verum
end;
A2214: for v2, v3, v4, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v0,v2,v3)))))
proof
let v2, v3, v4, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v0,v2,v3)))))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v3,(Tern (v0,v1,v4))))) = Tern (v2,(Tern (v0,v1,v4)),(Tern (v1,v3,(Tern (v0,v2,v3))))) by A2212; :: thesis: verum
end;
A2218: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v4,v1))))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v4,v1))))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3)))))
Tern (v0,v4,v1) = Tern (v1,v0,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v4,v1))))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3))))) by A2214; :: thesis: verum
end;
A2220: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3)))))
Tern (v0,v4,v1) = Tern (v0,v1,v4) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3))))) by A2218; :: thesis: verum
end;
A2222: for v0, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,v4,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3)))))
proof
let v0, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,v4,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3)))))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v2,v4,(Tern (v0,v1,v4))))) = Tern (v0,v4,(Tern (v1,v2,v3))) by A1876;
hence Tern (v0,v4,(Tern (v1,v2,v3))) = Tern (v1,(Tern (v2,v0,v4)),(Tern (v0,v4,(Tern (v1,v2,v3))))) by A2220; :: thesis: verum
end;
A2225: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,v1,v3) = Tern (v3,v0,v1) by A3;
hence Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v2,(Tern (v0,v1,v3)),(Tern (v0,v1,(Tern (v2,v3,v4))))) by A2222; :: thesis: verum
end;
A2227: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v0,v1,(Tern (v2,v3,v4)))))
Tern (v0,v1,v3) = Tern (v0,v3,v1) by A4;
hence Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v2,(Tern (v0,v3,v1)),(Tern (v0,v1,(Tern (v2,v3,v4))))) by A2225; :: thesis: verum
end;
A2232: for v101, v100, v103, v4, v3, v102 being Element of (BA2TBAA B) holds Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v102,(Tern (v100,v103,(Tern (v102,v3,v4))))))) = Tern (v100,(Tern (v3,v4,v103)),(Tern (v100,v102,v103)))
proof
let v101, v100, v103, v4, v3, v102 be Element of (BA2TBAA B); :: thesis: Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v102,(Tern (v100,v103,(Tern (v102,v3,v4))))))) = Tern (v100,(Tern (v3,v4,v103)),(Tern (v100,v102,v103)))
Tern (v100,v103,(Tern (v100,v102,(Tern (v3,v4,v103))))) = Tern (v100,v102,(Tern (v100,v103,(Tern (v102,v3,v4))))) by A1937;
hence Tern (v100,(Tern (v101,v102,v103)),(Tern (v100,v102,(Tern (v100,v103,(Tern (v102,v3,v4))))))) = Tern (v100,(Tern (v3,v4,v103)),(Tern (v100,v102,v103))) by A971; :: thesis: verum
end;
A2235: for v3, v0, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v4,v5)),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v4,v5,v3)),(Tern (v0,v2,v3)))
proof
now :: thesis: for v1, v0, v3, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v4,v5)),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v4,v5,v3)),(Tern (v0,v2,v3)))
let v1, v0, v3, v5, v4, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v2,v4,v5)),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v4,v5,v3)),(Tern (v0,v2,v3)))
Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v2,(Tern (v0,v3,(Tern (v2,v4,v5))))))) = Tern (v0,(Tern (v2,v4,v5)),(Tern (v0,v2,v3))) by A2052;
hence Tern (v0,(Tern (v2,v4,v5)),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v4,v5,v3)),(Tern (v0,v2,v3))) by A2232; :: thesis: verum
end;
hence for v3, v0, v5, v4, v2 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v2,v4,v5)),(Tern (v0,v2,v3))) = Tern (v0,(Tern (v4,v5,v3)),(Tern (v0,v2,v3))) ; :: thesis: verum
end;
A2238: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4))) = Tern (v0,(Tern (v4,v2,v3)),(Tern (v0,v1,v4)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4))) = Tern (v0,(Tern (v4,v2,v3)),(Tern (v0,v1,v4)))
Tern (v2,v3,v4) = Tern (v4,v2,v3) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v0,v1,v4))) = Tern (v0,(Tern (v4,v2,v3)),(Tern (v0,v1,v4))) by A2235; :: thesis: verum
end;
A2243: for v102, v4, v3, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v102,v4,v1)),v102) = Tern (v102,(Tern (v4,v2,v3)),(Tern (v102,v4,v1)))
proof
let v102, v4, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v102,v4,v1)),v102) = Tern (v102,(Tern (v4,v2,v3)),(Tern (v102,v4,v1)))
Tern (v102,(Tern (v1,v2,v3)),(Tern (v102,v4,v1))) = Tern (v102,(Tern (v4,v2,v3)),(Tern (v102,v4,v1))) by A2238;
hence Tern ((Tern (v1,v2,v3)),(Tern (v102,v4,v1)),v102) = Tern (v102,(Tern (v4,v2,v3)),(Tern (v102,v4,v1))) by A3; :: thesis: verum
end;
A2246: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,(Tern (v4,v1,v2)),(Tern (v3,v4,v0)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,(Tern (v4,v1,v2)),(Tern (v3,v4,v0)))
Tern (v3,v4,v0) = Tern (v0,v3,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,(Tern (v4,v1,v2)),(Tern (v3,v4,v0))) by A2243; :: thesis: verum
end;
A2248: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) = Tern (v3,(Tern (v4,v1,v2)),(Tern (v3,v4,v0)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) = Tern (v3,(Tern (v4,v1,v2)),(Tern (v3,v4,v0)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v3,v4)),v3) = Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) by A3;
hence Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v3,v4))) = Tern (v3,(Tern (v4,v1,v2)),(Tern (v3,v4,v0))) by A2246; :: thesis: verum
end;
A2251: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v3,v4,v2)),(Tern (v0,v4,v1)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v3,v4,v2)),(Tern (v0,v4,v1)))
Tern (v4,v2,v3) = Tern (v3,v4,v2) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v3,v4,v2)),(Tern (v0,v4,v1))) by A2248; :: thesis: verum
end;
A2253: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v4,v1)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v4,v1)))
Tern (v3,v4,v2) = Tern (v2,v3,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v0,v4,v1))) by A2251; :: thesis: verum
end;
A2255: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v0,v4)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v0,v4)))
Tern (v0,v4,v1) = Tern (v1,v0,v4) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v0,v4))) = Tern (v0,(Tern (v2,v3,v4)),(Tern (v1,v0,v4))) by A2253; :: thesis: verum
end;
A2260: for v3, v101, v102, v104, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),(Tern (v101,v102,(Tern (v1,v2,v104)))),(Tern (v1,v2,v104))) = Tern ((Tern (v1,v2,v3)),(Tern (v104,v101,v102)),(Tern (v104,(Tern (v1,v2,v3)),(Tern (v1,v2,v104)))))
proof
let v3, v101, v102, v104, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v3)),(Tern (v101,v102,(Tern (v1,v2,v104)))),(Tern (v1,v2,v104))) = Tern ((Tern (v1,v2,v3)),(Tern (v104,v101,v102)),(Tern (v104,(Tern (v1,v2,v3)),(Tern (v1,v2,v104)))))
Tern (v104,(Tern (v1,v2,v3)),(Tern (v1,v2,v104))) = Tern (v1,v2,v104) by A729;
hence Tern ((Tern (v1,v2,v3)),(Tern (v101,v102,(Tern (v1,v2,v104)))),(Tern (v1,v2,v104))) = Tern ((Tern (v1,v2,v3)),(Tern (v104,v101,v102)),(Tern (v104,(Tern (v1,v2,v3)),(Tern (v1,v2,v104))))) by A2255; :: thesis: verum
end;
A2263: for v2, v3, v4, v5, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v5)),(Tern (v3,v4,(Tern (v0,v1,v5))))) = Tern ((Tern (v0,v1,v2)),(Tern (v5,v3,v4)),(Tern (v5,(Tern (v0,v1,v2)),(Tern (v0,v1,v5)))))
proof
let v2, v3, v4, v5, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v5)),(Tern (v3,v4,(Tern (v0,v1,v5))))) = Tern ((Tern (v0,v1,v2)),(Tern (v5,v3,v4)),(Tern (v5,(Tern (v0,v1,v2)),(Tern (v0,v1,v5)))))
Tern ((Tern (v0,v1,v2)),(Tern (v3,v4,(Tern (v0,v1,v5)))),(Tern (v0,v1,v5))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v5)),(Tern (v3,v4,(Tern (v0,v1,v5))))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v5)),(Tern (v3,v4,(Tern (v0,v1,v5))))) = Tern ((Tern (v0,v1,v2)),(Tern (v5,v3,v4)),(Tern (v5,(Tern (v0,v1,v2)),(Tern (v0,v1,v5))))) by A2260; :: thesis: verum
end;
A2266: for v2, v4, v5, v3, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v5,v3,v4)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))))
proof
let v2, v4, v5, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v5,v3,v4)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))))
Tern (v3,v4,v5) = Tern (v5,v3,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v5,v3,v4)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))))) by A2263; :: thesis: verum
end;
A2268: for v2, v4, v5, v3, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v4,v5,v3)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))))
proof
let v2, v4, v5, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v4,v5,v3)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))))
Tern (v5,v3,v4) = Tern (v4,v5,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v4,v5,v3)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))))) by A2266; :: thesis: verum
end;
A2270: for v2, v4, v5, v3, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v4,v5,v3)),(Tern (v0,v1,v3)))
proof
let v2, v4, v5, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v4,v5,v3)),(Tern (v0,v1,v3)))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern (v0,v1,v3) by A729;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v4,v5,(Tern (v0,v1,v3))))) = Tern ((Tern (v0,v1,v2)),(Tern (v4,v5,v3)),(Tern (v0,v1,v3))) by A2268; :: thesis: verum
end;
A2273: for v104, v103, v4, v2, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v4)),(Tern ((Tern (v1,v2,v103)),v103,(Tern (v1,v2,v4)))),(Tern (v103,(Tern (v1,v2,v4)),v104))) = Tern ((Tern (v1,v2,v103)),(Tern (v1,v2,v4)),(Tern (v103,(Tern (v1,v2,v4)),v104)))
proof
let v104, v103, v4, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v2,v4)),(Tern ((Tern (v1,v2,v103)),v103,(Tern (v1,v2,v4)))),(Tern (v103,(Tern (v1,v2,v4)),v104))) = Tern ((Tern (v1,v2,v103)),(Tern (v1,v2,v4)),(Tern (v103,(Tern (v1,v2,v4)),v104)))
Tern ((Tern (v1,v2,v103)),(Tern (v1,v2,v103)),(Tern ((Tern (v1,v2,v103)),v103,(Tern (v1,v2,v4))))) = Tern ((Tern (v1,v2,v103)),v103,(Tern (v1,v2,v4))) by A889;
hence Tern ((Tern (v1,v2,v4)),(Tern ((Tern (v1,v2,v103)),v103,(Tern (v1,v2,v4)))),(Tern (v103,(Tern (v1,v2,v4)),v104))) = Tern ((Tern (v1,v2,v103)),(Tern (v1,v2,v4)),(Tern (v103,(Tern (v1,v2,v4)),v104))) by A2073; :: thesis: verum
end;
A2276: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern ((Tern (v0,v1,v3)),v3,(Tern (v0,v1,v2))) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3)))),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4))) by A2273; :: thesis: verum
end;
A2278: for v4, v3, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
proof
let v4, v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v1,v3))) = Tern (v0,v1,v3) by A729;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,(Tern (v0,v1,v2)),v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4))) by A2276; :: thesis: verum
end;
A2280: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
Tern (v3,(Tern (v0,v1,v2)),v4) = Tern (v3,v4,(Tern (v0,v1,v2))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4))) by A2278; :: thesis: verum
end;
A2282: for v2, v4, v3, v1, v0 being Element of (BA2TBAA B) holds Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
proof
let v2, v4, v3, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v1,v3)),(Tern (v3,v4,(Tern (v0,v1,v2))))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A881;
hence Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) = Tern ((Tern (v0,v1,v3)),(Tern (v0,v1,v2)),(Tern (v3,(Tern (v0,v1,v2)),v4))) by A2280; :: thesis: verum
end;
A2285: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v4)),(Tern (v3,v0,(Tern (v1,v2,v4)))))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v4)),(Tern (v3,v0,(Tern (v1,v2,v4)))))
Tern (v3,(Tern (v1,v2,v4)),v0) = Tern (v3,v0,(Tern (v1,v2,v4))) by A4;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v4)),(Tern (v3,v0,(Tern (v1,v2,v4))))) by A2282; :: thesis: verum
end;
A2287: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v3,v0,v4)),(Tern (v1,v2,v4)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v3,v0,v4)),(Tern (v1,v2,v4)))
Tern ((Tern (v1,v2,v3)),(Tern (v1,v2,v4)),(Tern (v3,v0,(Tern (v1,v2,v4))))) = Tern ((Tern (v1,v2,v3)),(Tern (v3,v0,v4)),(Tern (v1,v2,v4))) by A2270;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v3,v0,v4)),(Tern (v1,v2,v4))) by A2285; :: thesis: verum
end;
A2289: for v4, v0, v3, v2, v1 being Element of (BA2TBAA B) holds Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v4,v3,v0)),(Tern (v1,v2,v4)))
proof
let v4, v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis: Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v4,v3,v0)),(Tern (v1,v2,v4)))
Tern (v3,v0,v4) = Tern (v4,v3,v0) by A3;
hence Tern (v0,(Tern (v1,v2,v3)),(Tern (v1,v2,v4))) = Tern ((Tern (v1,v2,v3)),(Tern (v4,v3,v0)),(Tern (v1,v2,v4))) by A2287; :: thesis: verum
end;
A2294: for v101, v102, v4, v2, v104 being Element of (BA2TBAA B) holds Tern ((Tern (v101,v2,v102)),(Tern (v101,v102,(Tern (v104,v2,v4)))),(Tern (v104,(Tern (v101,v2,v102)),(Tern (v104,v101,v102))))) = Tern (v101,v102,(Tern (v104,v2,v4)))
proof
let v101, v102, v4, v2, v104 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v101,v2,v102)),(Tern (v101,v102,(Tern (v104,v2,v4)))),(Tern (v104,(Tern (v101,v2,v102)),(Tern (v104,v101,v102))))) = Tern (v101,v102,(Tern (v104,v2,v4)))
Tern (v104,(Tern (v101,v2,v102)),(Tern (v101,v102,(Tern (v104,v2,v4))))) = Tern (v101,v102,(Tern (v104,v2,v4))) by A2227;
hence Tern ((Tern (v101,v2,v102)),(Tern (v101,v102,(Tern (v104,v2,v4)))),(Tern (v104,(Tern (v101,v2,v102)),(Tern (v104,v101,v102))))) = Tern (v101,v102,(Tern (v104,v2,v4))) by A1863; :: thesis: verum
end;
A2297: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v4,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v4,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
Tern (v1,v4,v3) = Tern (v3,v1,v4) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v4,v3)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v3,v0,v2))))) = Tern (v0,v2,(Tern (v3,v1,v4))) by A2294; :: thesis: verum
end;
A2300: for v0, v2, v3, v4, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v4,v3)))),(Tern (v4,(Tern (v0,v1,v2)),(Tern (v4,v0,v2))))) = Tern (v0,v2,(Tern (v4,v1,v3)))
proof
let v0, v2, v3, v4, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v4,v3)))),(Tern (v4,(Tern (v0,v1,v2)),(Tern (v4,v0,v2))))) = Tern (v0,v2,(Tern (v4,v1,v3)))
Tern (v1,v3,v4) = Tern (v1,v4,v3) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v4,v3)))),(Tern (v4,(Tern (v0,v1,v2)),(Tern (v4,v0,v2))))) = Tern (v0,v2,(Tern (v4,v1,v3))) by A2297; :: thesis: verum
end;
A2303: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v2,v3,v0))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v2,v3,v0))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
Tern (v3,v0,v2) = Tern (v2,v3,v0) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v2,v3,v0))))) = Tern (v0,v2,(Tern (v3,v1,v4))) by A2300; :: thesis: verum
end;
A2305: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
Tern (v2,v3,v0) = Tern (v0,v2,v3) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))))) = Tern (v0,v2,(Tern (v3,v1,v4))) by A2303; :: thesis: verum
end;
A2307: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v3,v1,v4)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v3,v1,v4)))
Tern (v3,(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) = Tern (v0,v2,v3) by A1389;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v3,v1,v4))) by A2305; :: thesis: verum
end;
A2309: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v3,v1,v4)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,(Tern (v1,v3,v4)))),(Tern (v0,v2,v3))) = Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,(Tern (v1,v3,v4))))) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern (v0,v2,(Tern (v3,v1,v4))) by A2307; :: thesis: verum
end;
A2311: for v0, v2, v4, v3, v1 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v3,v4)),(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v3,v1,v4)))
proof
let v0, v2, v4, v3, v1 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v1,v3,v4)),(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v3,v1,v4)))
Tern ((Tern (v0,v1,v2)),(Tern (v0,v2,v3)),(Tern (v0,v2,(Tern (v1,v3,v4))))) = Tern ((Tern (v1,v3,v4)),(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) by A2102;
hence Tern ((Tern (v1,v3,v4)),(Tern (v0,v1,v2)),(Tern (v0,v2,v3))) = Tern (v0,v2,(Tern (v3,v1,v4))) by A2309; :: thesis: verum
end;
A2314: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v2,v1)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v2,v1)))
Tern (v0,v2,v1) = Tern (v1,v0,v2) by A3;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v2,v1))) by A2311; :: thesis: verum
end;
A2316: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v1,v2)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v1,v2))) by A2314; :: thesis: verum
end;
A2319: for v3, v4, v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v3,v4,(Tern (v0,v1,v2))) = Tern ((Tern (v3,v4,v1)),(Tern (v0,v1,v2)),(Tern (v3,v0,v4)))
proof
let v3, v4, v2, v1, v0 be Element of (BA2TBAA B); :: thesis: Tern (v3,v4,(Tern (v0,v1,v2))) = Tern ((Tern (v3,v4,v1)),(Tern (v0,v1,v2)),(Tern (v3,v0,v4)))
Tern ((Tern (v0,v1,v2)),(Tern (v3,v0,v4)),(Tern (v3,v4,v1))) = Tern (v3,v4,(Tern (v0,v1,v2))) by A2316;
hence Tern (v3,v4,(Tern (v0,v1,v2))) = Tern ((Tern (v3,v4,v1)),(Tern (v0,v1,v2)),(Tern (v3,v0,v4))) by A3; :: thesis: verum
end;
A2322: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,v2)))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,v2)))
Tern (v0,v2,v1) = Tern (v0,v1,v2) by A4;
hence Tern (v0,v1,(Tern (v2,v3,v4))) = Tern ((Tern (v0,v1,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) by A2319; :: thesis: verum
end;
A2324: for v0, v1, v4, v3, v2 being Element of (BA2TBAA B) holds Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
proof
let v0, v1, v4, v3, v2 be Element of (BA2TBAA B); :: thesis: Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2)))
Tern ((Tern (v0,v1,v3)),(Tern (v2,v3,v4)),(Tern (v0,v1,v2))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A2289;
hence Tern (v0,v1,(Tern (v2,v3,v4))) = Tern (v4,(Tern (v0,v1,v3)),(Tern (v0,v1,v2))) by A2322; :: thesis: verum
end;
not Tern (c1,c2,(Tern (c5,c3,c4))) = Tern (c1,c2,(Tern (c3,c4,c5))) by A32, A2324;
hence contradiction by A3; :: thesis: verum