let B be Boolean Lattice; :: thesis:
assume A1: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = ((v0 "\/" v1) "/\" (v1 "\/" v2)) "/\" (v0 "\/" v2) ; :: thesis:
assume A4: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v2) = (v0 "\/" v1) "/\" (v0 "\/" v2) ; :: thesis:
assume A6: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" v2) = (v0 "/\" v1) "\/" (v0 "/\" v2) ; :: thesis:
assume A8: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "\/" v2 = v0 "\/" (v1 "\/" v2) ; :: thesis:
assume A14: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" v2 = v0 "/\" (v1 "/\" v2) ; :: thesis:
assume not for v1, v2, v3, v4 being Element of (BA2TBAA B) holds Tern ((Tern (v1,v2,v3)),v2,v4) = Tern (v1,v2,(Tern (v3,v2,v4))) ; :: thesis:
then consider c1, c2, c3, c4 being Element of (BA2TBAA B) such that
A20: not Tern ((Tern (c1,c2,c3)),c2,c4) = Tern (c1,c2,(Tern (c3,c2,c4))) ;
not Tern ((((c1 "\/" c2) "/\" (c2 "\/" c3)) "/\" (c1 "\/" c3)),c2,c4) = Tern (c1,c2,(Tern (c3,c2,c4))) by A1, A20;
then not Tern (((c1 "\/" c2) "/\" ((c2 "\/" c3) "/\" (c1 "\/" c3))),c2,c4) = Tern (c1,c2,(Tern (c3,c2,c4))) by A14;
then AA: not ((((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))) "\/" c2) "/\" (c2 "\/" c4)) "/\" (((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))) "\/" c4) = Tern (c1,c2,(Tern (c3,c2,c4))) by A1;
A38: not (c2 "\/" (c4 "/\" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))))) "/\" (c4 "\/" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3)))) = Tern (c1,c2,(Tern (c3,c2,c4))) by A4, AA;
A42: not (c4 "\/" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3)))) "/\" (c2 "\/" (c4 "/\" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))))) = Tern (c1,c2,(((c3 "\/" c2) "/\" (c2 "\/" c4)) "/\" (c3 "\/" c4))) by A1, A38;
A48: not (c4 "\/" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3)))) "/\" (c2 "\/" (c4 "/\" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))))) = Tern (c1,c2,((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4)))) by A4, A42;
A52: not (c4 "\/" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3)))) "/\" (c2 "\/" (c4 "/\" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))))) = (c1 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4)))) "/\" ((c1 "\/" c2) "/\" (c2 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A1, A48;
A56: not (c4 "\/" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3)))) "/\" (c2 "\/" (c4 "/\" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))))) = (c1 "\/" c2) "/\" ((c1 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4)))) "/\" (c2 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A52, A14;
A63: for v2, v1, v0 being Element of (BA2TBAA B) holds Tern (v0,v1,v2) = (v0 "\/" v2) "/\" (v1 "\/" (v0 "/\" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence Tern (v0,v1,v2) = (v0 "\/" v2) "/\" (v1 "\/" (v0 "/\" v2)) by A1; :: thesis:

end;

A69: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "/\" v1) "\/" v101) "/\" (v0 "/\" (v1 "\/" v2)) = (v0 "/\" v1) "\/" (v101 "/\" (v0 "/\" v2))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" v2) = v0 "/\" (v1 "\/" v2) by A6;
hence ((v0 "/\" v1) "\/" v101) "/\" (v0 "/\" (v1 "\/" v2)) = (v0 "/\" v1) "\/" (v101 "/\" (v0 "/\" v2)) by A4; :: thesis:

end;

A75: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v1 "/\" ((v2 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v1 "/\" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" ((v2 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v0 "\/" (v1 "/\" v2)) "/\" (v1 "/\" (v2 "\/" v3)) by A14;
hence v1 "/\" ((v2 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v1 "/\" v3)) by A69; :: thesis:

end;

A78: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v0 "/\" v1))) = (v0 "/\" v1) "\/" (v0 "/\" (v2 "/\" v3))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v3) = v3 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v0 "/\" v1))) = (v0 "/\" v1) "\/" (v0 "/\" (v2 "/\" v3)) by A75; :: thesis:

end;

A82: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v3 "/\" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" (v3 "/\" v2)) = v0 "/\" (v1 "\/" (v3 "/\" v2)) by A6;
hence v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v3 "/\" v2)) by A78; :: thesis:

end;

A85: for v102, v1, v101 being Element of (BA2TBAA B) holds ((v101 "/\" v1) "\/" v101) "/\" ((v101 "/\" v1) "\/" v102) = v101 "/\" (v1 "\/" v102)

proof

let v102, v1, v101 be Element of (BA2TBAA B); :: thesis:
(v101 "/\" v1) "\/" (v101 "/\" v102) = v101 "/\" (v1 "\/" v102) by A6;
hence ((v101 "/\" v1) "\/" v101) "/\" ((v101 "/\" v1) "\/" v102) = v101 "/\" (v1 "\/" v102) by A4; :: thesis:

end;

A93: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "\/" v1) "/\" v101) "\/" (v0 "\/" (v1 "/\" v2)) = (v0 "\/" v1) "/\" (v101 "\/" (v0 "\/" v2))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence ((v0 "\/" v1) "/\" v101) "\/" (v0 "\/" (v1 "/\" v2)) = (v0 "\/" v1) "/\" (v101 "\/" (v0 "\/" v2)) by A6; :: thesis:

end;

A99: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v1 "\/" ((v2 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v1 "\/" v2) "/\" (v0 "\/" (v1 "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" ((v2 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v0 "/\" (v1 "\/" v2)) "\/" (v1 "\/" (v2 "/\" v3)) by A8;
hence v1 "\/" ((v2 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v1 "\/" v2) "/\" (v0 "\/" (v1 "\/" v3)) by A93; :: thesis:

end;

A102: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v1))) = (v0 "\/" v1) "/\" (v0 "\/" (v2 "\/" v3))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v2 "\/" v3) = v3 "\/" (v0 "\/" v2) by A8;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v1))) = (v0 "\/" v1) "/\" (v0 "\/" (v2 "\/" v3)) by A99; :: thesis:

end;

A106: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v1))) = v0 "\/" (v1 "/\" (v3 "\/" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v3 "\/" v2)) = v0 "\/" (v1 "/\" (v3 "\/" v2)) by A4;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v1))) = v0 "\/" (v1 "/\" (v3 "\/" v2)) by A102; :: thesis:

end;

A109: for v102, v2, v1, v100 being Element of (BA2TBAA B) holds (v2 "\/" (v100 "\/" v1)) "/\" (v100 "\/" v102) = v100 "\/" ((v1 "\/" v2) "/\" v102)

proof

let v102, v2, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v1 "\/" v2) = v2 "\/" (v100 "\/" v1) by A8;
hence (v2 "\/" (v100 "\/" v1)) "/\" (v100 "\/" v102) = v100 "\/" ((v1 "\/" v2) "/\" v102) by A4; :: thesis:

end;

A117: for v102, v0, v100, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" v100)) "/\" (v100 "\/" v102) = v100 "\/" ((v0 "\/" v1) "/\" v102)

proof

let v102, v0, v100, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "\/" v100) = v100 "\/" (v0 "\/" v1) by A8;
hence (v0 "\/" (v1 "\/" v100)) "/\" (v100 "\/" v102) = v100 "\/" ((v0 "\/" v1) "/\" v102) by A4; :: thesis:

end;

A123: for v102, v2, v1, v100 being Element of (BA2TBAA B) holds (v2 "/\" (v100 "/\" v1)) "\/" (v100 "/\" v102) = v100 "/\" ((v1 "/\" v2) "\/" v102)

proof

let v102, v2, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v1 "/\" v2) = v2 "/\" (v100 "/\" v1) by A14;
hence (v2 "/\" (v100 "/\" v1)) "\/" (v100 "/\" v102) = v100 "/\" ((v1 "/\" v2) "\/" v102) by A6; :: thesis:

end;

A131: for v102, v0, v100, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" v100)) "\/" (v100 "/\" v102) = v100 "/\" ((v0 "/\" v1) "\/" v102)

proof

let v102, v0, v100, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v100) = v100 "/\" (v0 "/\" v1) by A14;
hence (v0 "/\" (v1 "/\" v100)) "\/" (v100 "/\" v102) = v100 "/\" ((v0 "/\" v1) "\/" v102) by A6; :: thesis:

end;

A137: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "\/" v1) "/\" v101) "\/" (v1 "\/" (v0 "/\" v2)) = (v0 "\/" v1) "/\" (v101 "\/" (v1 "\/" v2))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence ((v0 "\/" v1) "/\" v101) "\/" (v1 "\/" (v0 "/\" v2)) = (v0 "\/" v1) "/\" (v101 "\/" (v1 "\/" v2)) by A6; :: thesis:

end;

A143: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v2 "\/" ((v1 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v1 "\/" v2) "/\" (v0 "\/" (v2 "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "\/" ((v1 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v0 "/\" (v1 "\/" v2)) "\/" (v2 "\/" (v1 "/\" v3)) by A8;
hence v2 "\/" ((v1 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v1 "\/" v2) "/\" (v0 "\/" (v2 "\/" v3)) by A137; :: thesis:

end;

A146: for v2, v3, v0, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v1 "\/" v0))) = (v1 "\/" v0) "/\" (v0 "\/" (v2 "\/" v3))

proof

let v2, v3, v0, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v2 "\/" v3) = v3 "\/" (v0 "\/" v2) by A8;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v1 "\/" v0))) = (v1 "\/" v0) "/\" (v0 "\/" (v2 "\/" v3)) by A143; :: thesis:

end;

A150: for v2, v3, v0, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v1 "\/" v0))) = v0 "\/" (v1 "/\" (v3 "\/" v2))

proof

let v2, v3, v0, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v0) "/\" (v0 "\/" (v3 "\/" v2)) = v0 "\/" (v1 "/\" (v3 "\/" v2)) by A4;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v1 "\/" v0))) = v0 "\/" (v1 "/\" (v3 "\/" v2)) by A146; :: thesis:

end;

A153: for v2, v100, v1, v0 being Element of (BA2TBAA B) holds (v100 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v1 "\/" v2)) = (v0 "/\" v1) "\/" (v100 "/\" (v0 "/\" v2))

proof

let v2, v100, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" v2) = v0 "/\" (v1 "\/" v2) by A6;
hence (v100 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v1 "\/" v2)) = (v0 "/\" v1) "\/" (v100 "/\" (v0 "/\" v2)) by A4; :: thesis:

end;

A156: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v1 "/\" ((v2 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v1 "/\" v3))

proof

end;

A159: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v3 "/\" v2)) = (v0 "/\" v1) "\/" (v3 "/\" (v0 "/\" v2))

proof

let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v3 "/\" v2)) by A82;
hence v0 "/\" (v1 "\/" (v3 "/\" v2)) = (v0 "/\" v1) "\/" (v3 "/\" (v0 "/\" v2)) by A156; :: thesis:

end;

A164: for v102, v2, v1, v100 being Element of (BA2TBAA B) holds (v2 "\/" (v100 "\/" v1)) "/\" ((v1 "\/" v2) "\/" v102) = (v1 "\/" v2) "\/" (v100 "/\" v102)

proof

let v102, v2, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v1 "\/" v2) = v2 "\/" (v100 "\/" v1) by A8;
hence (v2 "\/" (v100 "\/" v1)) "/\" ((v1 "\/" v2) "\/" v102) = (v1 "\/" v2) "\/" (v100 "/\" v102) by A4; :: thesis:

end;

A171: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" v2)) "/\" (v2 "\/" (v3 "\/" v0)) = (v2 "\/" v0) "\/" (v1 "/\" v3)

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v3 "\/" (v0 "\/" v2) = v2 "\/" (v3 "\/" v0) by A8;
hence (v0 "\/" (v1 "\/" v2)) "/\" (v2 "\/" (v3 "\/" v0)) = (v2 "\/" v0) "\/" (v1 "/\" v3) by A164; :: thesis:

end;

A175: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" v2)) "/\" (v0 "\/" (v3 "\/" v2)) = (v2 "\/" v0) "\/" (v1 "/\" v3)

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v3 "\/" v2) = v2 "\/" (v0 "\/" v3) by A8;
hence (v0 "\/" (v1 "\/" v2)) "/\" (v0 "\/" (v3 "\/" v2)) = (v2 "\/" v0) "\/" (v1 "/\" v3) by A171; :: thesis:

end;

A179: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "\/" v2) "/\" (v2 "\/" v3)) = (v2 "\/" v0) "\/" (v1 "/\" v3)

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" v2)) "/\" (v0 "\/" (v2 "\/" v3)) = v0 "\/" ((v1 "\/" v2) "/\" (v2 "\/" v3)) by A4;
hence v0 "\/" ((v1 "\/" v2) "/\" (v2 "\/" v3)) = (v2 "\/" v0) "\/" (v1 "/\" v3) by A175; :: thesis:

end;

A181: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds v0 "\/" (v2 "\/" (v1 "/\" v3)) = (v2 "\/" v0) "\/" (v1 "/\" v3)

proof

let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v2) "/\" (v2 "\/" v3) = v2 "\/" (v1 "/\" v3) by A4;
hence v0 "\/" (v2 "\/" (v1 "/\" v3)) = (v2 "\/" v0) "\/" (v1 "/\" v3) by A179; :: thesis:

end;

A188: for v0, v102, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v1 "\/" v2) "/\" v102) = v102 "/\" (v1 "\/" (v0 "/\" v2))

proof

let v0, v102, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence (v0 "\/" v1) "/\" ((v1 "\/" v2) "/\" v102) = v102 "/\" (v1 "\/" (v0 "/\" v2)) by A14; :: thesis:

end;

A194: for v2, v0, v3, v1 being Element of (BA2TBAA B) holds v2 "/\" ((v1 "\/" v3) "/\" (v0 "\/" v1)) = v2 "/\" (v1 "\/" (v0 "/\" v3))

proof

let v2, v0, v3, v1 be Element of (BA2TBAA B); :: thesis:
v2 "/\" ((v1 "\/" v3) "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v2 "/\" (v1 "\/" v3)) by A14;
hence v2 "/\" ((v1 "\/" v3) "/\" (v0 "\/" v1)) = v2 "/\" (v1 "\/" (v0 "/\" v3)) by A188; :: thesis:

end;

A198: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "\/" v1) "\/" v101) "/\" (v101 "\/" (v1 "\/" v2)) = v101 "\/" (v1 "\/" (v0 "/\" v2))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence ((v0 "\/" v1) "\/" v101) "/\" (v101 "\/" (v1 "\/" v2)) = v101 "\/" (v1 "\/" (v0 "/\" v2)) by A4; :: thesis:

end;

A204: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds (v2 "\/" (v0 "\/" v1)) "/\" (v0 "\/" (v2 "\/" v3)) = v0 "\/" (v2 "\/" (v1 "/\" v3))

proof

let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "\/" v2) = v2 "\/" (v0 "\/" v1) by A8;
hence (v2 "\/" (v0 "\/" v1)) "/\" (v0 "\/" (v2 "\/" v3)) = v0 "\/" (v2 "\/" (v1 "/\" v3)) by A198; :: thesis:

end;

A210: for v3, v1, v0, v2 being Element of (BA2TBAA B) holds (v1 "\/" (v2 "\/" v0)) "/\" (v2 "\/" (v0 "\/" v3)) = v2 "\/" (v0 "\/" (v1 "/\" v3))

proof

let v3, v1, v0, v2 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v2 "\/" v0) = v0 "\/" (v1 "\/" v2) by A8;
hence (v1 "\/" (v2 "\/" v0)) "/\" (v2 "\/" (v0 "\/" v3)) = v2 "\/" (v0 "\/" (v1 "/\" v3)) by A204; :: thesis:

end;

A216: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" v2)) "/\" (v1 "\/" (v3 "\/" v2)) = v2 "\/" (v1 "\/" (v0 "/\" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v3 "\/" v2) = v2 "\/" (v1 "\/" v3) by A8;
hence (v0 "\/" (v1 "\/" v2)) "/\" (v1 "\/" (v3 "\/" v2)) = v2 "\/" (v1 "\/" (v0 "/\" v3)) by A210; :: thesis:

end;

A220: for v1, v0, v3, v2 being Element of (BA2TBAA B) holds v1 "\/" ((v2 "\/" v3) "/\" (v0 "\/" v2)) = v2 "\/" (v1 "\/" (v0 "/\" v3))

proof

let v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" v2)) "/\" (v1 "\/" (v2 "\/" v3)) = v1 "\/" ((v2 "\/" v3) "/\" (v0 "\/" v2)) by A109;
hence v1 "\/" ((v2 "\/" v3) "/\" (v0 "\/" v2)) = v2 "\/" (v1 "\/" (v0 "/\" v3)) by A216; :: thesis:

end;

A223: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "\/" v2) "/\" (v3 "\/" v1)) = v0 "\/" ((v3 "/\" v2) "\/" v1)

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v3 "/\" v2) "\/" v1) = v1 "\/" (v0 "\/" (v3 "/\" v2)) by A8;
hence v0 "\/" ((v1 "\/" v2) "/\" (v3 "\/" v1)) = v0 "\/" ((v3 "/\" v2) "\/" v1) by A220; :: thesis:

end;

A228: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "/\" v1) "\/" v101) "/\" (v1 "/\" (v0 "\/" v2)) = (v0 "/\" v1) "\/" (v101 "/\" (v1 "/\" v2))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v1 "/\" v2) = v1 "/\" (v0 "\/" v2) by A6;
hence ((v0 "/\" v1) "\/" v101) "/\" (v1 "/\" (v0 "\/" v2)) = (v0 "/\" v1) "\/" (v101 "/\" (v1 "/\" v2)) by A4; :: thesis:

end;

A234: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v2 "/\" ((v1 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v2 "/\" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "/\" ((v1 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v0 "\/" (v1 "/\" v2)) "/\" (v2 "/\" (v1 "\/" v3)) by A14;
hence v2 "/\" ((v1 "\/" v3) "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v2 "/\" v3)) by A228; :: thesis:

end;

A237: for v2, v3, v0, v1 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v1 "/\" v0))) = (v1 "/\" v0) "\/" (v0 "/\" (v2 "/\" v3))

proof

let v2, v3, v0, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v3) = v3 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v1 "/\" v0))) = (v1 "/\" v0) "\/" (v0 "/\" (v2 "/\" v3)) by A234; :: thesis:

end;

A241: for v2, v3, v0, v1 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v1 "/\" v0))) = v0 "/\" (v1 "\/" (v3 "/\" v2))

proof

let v2, v3, v0, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v0) "\/" (v0 "/\" (v3 "/\" v2)) = v0 "/\" (v1 "\/" (v3 "/\" v2)) by A6;
hence v0 "/\" ((v1 "\/" v2) "/\" (v3 "\/" (v1 "/\" v0))) = v0 "/\" (v1 "\/" (v3 "/\" v2)) by A237; :: thesis:

end;

A244: for v102, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "/\" v2)) "\/" ((v0 "\/" v2) "/\" v102) = (v0 "\/" v2) "/\" ((v0 "\/" v1) "\/" v102)

proof

let v102, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence (v0 "\/" (v1 "/\" v2)) "\/" ((v0 "\/" v2) "/\" v102) = (v0 "\/" v2) "/\" ((v0 "\/" v1) "\/" v102) by A6; :: thesis:

end;

A249: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = (v0 "\/" v2) "/\" ((v0 "\/" v1) "\/" v3)

proof

let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "/\" v2)) "\/" (v3 "/\" (v0 "\/" v2)) = v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) by A181;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = (v0 "\/" v2) "/\" ((v0 "\/" v1) "\/" v3) by A244; :: thesis:

end;

A253: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = (v0 "\/" v2) "/\" (v1 "\/" (v3 "\/" v0))

proof

let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis:
v3 "\/" (v0 "\/" v1) = v1 "\/" (v3 "\/" v0) by A8;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = (v0 "\/" v2) "/\" (v1 "\/" (v3 "\/" v0)) by A249; :: thesis:

end;

A257: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = (v0 "\/" v2) "/\" (v0 "\/" (v3 "\/" v1))

proof

let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v3 "\/" v1) = v1 "\/" (v0 "\/" v3) by A8;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = (v0 "\/" v2) "/\" (v0 "\/" (v3 "\/" v1)) by A253; :: thesis:

end;

A261: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = v0 "\/" (v2 "/\" (v1 "\/" v3))

proof

let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v2) "/\" (v0 "\/" (v1 "\/" v3)) = v0 "\/" (v2 "/\" (v1 "\/" v3)) by A4;
hence v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v2))) = v0 "\/" (v2 "/\" (v1 "\/" v3)) by A257; :: thesis:

end;

A264: for v2, v100, v1, v0 being Element of (BA2TBAA B) holds (v100 "/\" (v0 "\/" v1)) "\/" (v0 "\/" (v1 "/\" v2)) = (v0 "\/" v1) "/\" (v100 "\/" (v0 "\/" v2))

proof

let v2, v100, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence (v100 "/\" (v0 "\/" v1)) "\/" (v0 "\/" (v1 "/\" v2)) = (v0 "\/" v1) "/\" (v100 "\/" (v0 "\/" v2)) by A6; :: thesis:

end;

A267: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v1 "\/" ((v2 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v1 "\/" v2) "/\" (v0 "\/" (v1 "\/" v3))

proof

end;

A270: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v3 "\/" v2)) = (v0 "\/" v1) "/\" (v3 "\/" (v0 "\/" v2))

proof

let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v0 "\/" v1))) = v0 "\/" (v1 "/\" (v3 "\/" v2)) by A106;
hence v0 "\/" (v1 "/\" (v3 "\/" v2)) = (v0 "\/" v1) "/\" (v3 "\/" (v0 "\/" v2)) by A267; :: thesis:

end;

A275: for v102, v2, v1, v100 being Element of (BA2TBAA B) holds (v2 "/\" (v100 "/\" v1)) "\/" ((v1 "/\" v2) "/\" v102) = (v1 "/\" v2) "/\" (v100 "\/" v102)

proof

let v102, v2, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v1 "/\" v2) = v2 "/\" (v100 "/\" v1) by A14;
hence (v2 "/\" (v100 "/\" v1)) "\/" ((v1 "/\" v2) "/\" v102) = (v1 "/\" v2) "/\" (v100 "\/" v102) by A6; :: thesis:

end;

A282: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" v2)) "\/" (v2 "/\" (v3 "/\" v0)) = (v2 "/\" v0) "/\" (v1 "\/" v3)

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v3 "/\" (v0 "/\" v2) = v2 "/\" (v3 "/\" v0) by A14;
hence (v0 "/\" (v1 "/\" v2)) "\/" (v2 "/\" (v3 "/\" v0)) = (v2 "/\" v0) "/\" (v1 "\/" v3) by A275; :: thesis:

end;

A286: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" v2)) "\/" (v0 "/\" (v3 "/\" v2)) = (v2 "/\" v0) "/\" (v1 "\/" v3)

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v3 "/\" v2) = v2 "/\" (v0 "/\" v3) by A14;
hence (v0 "/\" (v1 "/\" v2)) "\/" (v0 "/\" (v3 "/\" v2)) = (v2 "/\" v0) "/\" (v1 "\/" v3) by A282; :: thesis:

end;

A290: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "/\" v2) "\/" (v2 "/\" v3)) = (v2 "/\" v0) "/\" (v1 "\/" v3)

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v2)) "\/" (v0 "/\" (v2 "/\" v3)) = v0 "/\" ((v1 "/\" v2) "\/" (v2 "/\" v3)) by A6;
hence v0 "/\" ((v1 "/\" v2) "\/" (v2 "/\" v3)) = (v2 "/\" v0) "/\" (v1 "\/" v3) by A286; :: thesis:

end;

A292: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds v0 "/\" (v2 "/\" (v1 "\/" v3)) = (v2 "/\" v0) "/\" (v1 "\/" v3)

proof

let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v2) "\/" (v2 "/\" v3) = v2 "/\" (v1 "\/" v3) by A6;
hence v0 "/\" (v2 "/\" (v1 "\/" v3)) = (v2 "/\" v0) "/\" (v1 "\/" v3) by A290; :: thesis:

end;

A299: for v2, v100, v1, v0 being Element of (BA2TBAA B) holds (v100 "/\" (v0 "\/" v1)) "\/" (v1 "\/" (v0 "/\" v2)) = (v0 "\/" v1) "/\" (v100 "\/" (v1 "\/" v2))

proof

let v2, v100, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence (v100 "/\" (v0 "\/" v1)) "\/" (v1 "\/" (v0 "/\" v2)) = (v0 "\/" v1) "/\" (v100 "\/" (v1 "\/" v2)) by A6; :: thesis:

end;

A302: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v2 "\/" ((v1 "/\" v3) "\/" (v0 "/\" (v1 "\/" v2))) = (v1 "\/" v2) "/\" (v0 "\/" (v2 "\/" v3))

proof

end;

A305: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v3 "\/" v2)) = (v1 "\/" v0) "/\" (v3 "\/" (v0 "\/" v2))

proof

let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "/\" v2) "\/" (v3 "/\" (v1 "\/" v0))) = v0 "\/" (v1 "/\" (v3 "\/" v2)) by A150;
hence v0 "\/" (v1 "/\" (v3 "\/" v2)) = (v1 "\/" v0) "/\" (v3 "\/" (v0 "\/" v2)) by A302; :: thesis:

end;

A311: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "/\" v1) "/\" v101) "\/" (v101 "/\" (v1 "/\" v2)) = v101 "/\" (v1 "/\" (v0 "\/" v2))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v1 "/\" v2) = v1 "/\" (v0 "\/" v2) by A6;
hence ((v0 "/\" v1) "/\" v101) "\/" (v101 "/\" (v1 "/\" v2)) = v101 "/\" (v1 "/\" (v0 "\/" v2)) by A6; :: thesis:

end;

A317: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds (v2 "/\" (v0 "/\" v1)) "\/" (v0 "/\" (v2 "/\" v3)) = v0 "/\" (v2 "/\" (v1 "\/" v3))

proof

let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v2) = v2 "/\" (v0 "/\" v1) by A14;
hence (v2 "/\" (v0 "/\" v1)) "\/" (v0 "/\" (v2 "/\" v3)) = v0 "/\" (v2 "/\" (v1 "\/" v3)) by A311; :: thesis:

end;

A323: for v3, v1, v0, v2 being Element of (BA2TBAA B) holds (v1 "/\" (v2 "/\" v0)) "\/" (v2 "/\" (v0 "/\" v3)) = v2 "/\" (v0 "/\" (v1 "\/" v3))

proof

let v3, v1, v0, v2 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v2 "/\" v0) = v0 "/\" (v1 "/\" v2) by A14;
hence (v1 "/\" (v2 "/\" v0)) "\/" (v2 "/\" (v0 "/\" v3)) = v2 "/\" (v0 "/\" (v1 "\/" v3)) by A317; :: thesis:

end;

A329: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" v2)) "\/" (v1 "/\" (v3 "/\" v2)) = v2 "/\" (v1 "/\" (v0 "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v3 "/\" v2) = v2 "/\" (v1 "/\" v3) by A14;
hence (v0 "/\" (v1 "/\" v2)) "\/" (v1 "/\" (v3 "/\" v2)) = v2 "/\" (v1 "/\" (v0 "\/" v3)) by A323; :: thesis:

end;

A333: for v1, v0, v3, v2 being Element of (BA2TBAA B) holds v1 "/\" ((v2 "/\" v3) "\/" (v0 "/\" v2)) = v2 "/\" (v1 "/\" (v0 "\/" v3))

proof

let v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v2)) "\/" (v1 "/\" (v2 "/\" v3)) = v1 "/\" ((v2 "/\" v3) "\/" (v0 "/\" v2)) by A123;
hence v1 "/\" ((v2 "/\" v3) "\/" (v0 "/\" v2)) = v2 "/\" (v1 "/\" (v0 "\/" v3)) by A329; :: thesis:

end;

A336: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "/\" v2) "\/" (v3 "/\" v1)) = v0 "/\" ((v3 "\/" v2) "/\" v1)

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v3 "\/" v2) "/\" v1) = v1 "/\" (v0 "/\" (v3 "\/" v2)) by A14;
hence v0 "/\" ((v1 "/\" v2) "\/" (v3 "/\" v1)) = v0 "/\" ((v3 "\/" v2) "/\" v1) by A333; :: thesis:

end;

A341: for v102, v103, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v102 "/\" v103) = (v0 "/\" v1) "\/" ((v0 "/\" v2) "\/" (v102 "/\" v103))

proof

let v102, v103, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" v2) = v0 "/\" (v1 "\/" v2) by A6;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v102 "/\" v103) = (v0 "/\" v1) "\/" ((v0 "/\" v2) "\/" (v102 "/\" v103)) by A181; :: thesis:

end;

A346: for v102, v0, v1, v3, v2 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" (v2 "/\" v3))) "/\" ((v2 "/\" v3) "\/" v102) = (v2 "/\" v3) "\/" ((v0 "\/" v1) "/\" v102)

proof

let v102, v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v2 "/\" v3) = v0 "\/" (v1 "\/" (v2 "/\" v3)) by A181;
hence (v0 "\/" (v1 "\/" (v2 "/\" v3))) "/\" ((v2 "/\" v3) "\/" v102) = (v2 "/\" v3) "\/" ((v0 "\/" v1) "/\" v102) by A4; :: thesis:

end;

A354: for v102, v103, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "/\" v2)) "/\" (v102 "\/" v103) = (v0 "\/" v1) "/\" ((v0 "\/" v2) "/\" (v102 "\/" v103))

proof

let v102, v103, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence (v0 "\/" (v1 "/\" v2)) "/\" (v102 "\/" v103) = (v0 "\/" v1) "/\" ((v0 "\/" v2) "/\" (v102 "\/" v103)) by A292; :: thesis:

end;

A360: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" ((c1 "\/" c2) "/\" ((c1 "\/" c3) "/\" (c2 "\/" c3))))) = (c1 "\/" c2) "/\" ((c1 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4)))) "/\" (c2 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A354, A56;
A362: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" ((c1 "\/" (c2 "/\" c3)) "/\" (c2 "\/" c3)))) = (c1 "\/" c2) "/\" ((c1 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4)))) "/\" (c2 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A354, A360;
A368: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3))))) = (c2 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4)))) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A362, A354;
A371: for v102, v103, v100 being Element of (BA2TBAA B) holds v100 "/\" (v103 "\/" (v102 "/\" (v100 "/\" v103))) = v100 "/\" (v103 "\/" (v103 "/\" v102))

proof

let v102, v103, v100 be Element of (BA2TBAA B); :: thesis:
(v103 "\/" v102) "/\" (v103 "\/" (v100 "/\" v103)) = v103 "\/" (v102 "/\" (v100 "/\" v103)) by A4;
hence v100 "/\" (v103 "\/" (v102 "/\" (v100 "/\" v103))) = v100 "/\" (v103 "\/" (v103 "/\" v102)) by A82; :: thesis:

end;

A374: for v1, v0, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v1 "/\" (v2 "/\" v0))) = v0 "/\" (v1 "\/" (v1 "/\" v2))

proof

let v1, v0, v2 be Element of (BA2TBAA B); :: thesis:
v2 "/\" (v0 "/\" v1) = v1 "/\" (v2 "/\" v0) by A14;
hence v0 "/\" (v1 "\/" (v1 "/\" (v2 "/\" v0))) = v0 "/\" (v1 "\/" (v1 "/\" v2)) by A371; :: thesis:

end;

A378: for v0, v1, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v1))) = v0 "/\" (v1 "\/" (v1 "/\" v2))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v1) = v1 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v1))) = v0 "/\" (v1 "\/" (v1 "/\" v2)) by A374; :: thesis:

end;

A383: for v102, v100, v101, v1 being Element of (BA2TBAA B) holds v100 "/\" ((v101 "\/" v102) "/\" (v100 "/\" (v1 "\/" v101))) = v100 "/\" (v101 "\/" ((v100 "/\" v1) "/\" v102))

proof

let v102, v100, v101, v1 be Element of (BA2TBAA B); :: thesis:
(v100 "/\" v1) "\/" (v100 "/\" v101) = v100 "/\" (v1 "\/" v101) by A6;
hence v100 "/\" ((v101 "\/" v102) "/\" (v100 "/\" (v1 "\/" v101))) = v100 "/\" (v101 "\/" ((v100 "/\" v1) "/\" v102)) by A82; :: thesis:

end;

A388: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v1 "\/" v3) "/\" (v1 "\/" v2))) = v0 "/\" (v1 "\/" ((v0 "/\" v3) "/\" v2))

proof

let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "\/" v3) "/\" (v1 "\/" v2)) = (v1 "\/" v2) "/\" (v0 "/\" (v1 "\/" v3)) by A14;
hence v0 "/\" (v0 "/\" ((v1 "\/" v3) "/\" (v1 "\/" v2))) = v0 "/\" (v1 "\/" ((v0 "/\" v3) "/\" v2)) by A383; :: thesis:

end;

A391: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "\/" (v2 "/\" v3))) = v0 "/\" (v1 "\/" ((v0 "/\" v2) "/\" v3))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v2) "/\" (v1 "\/" v3) = v1 "\/" (v2 "/\" v3) by A4;
hence v0 "/\" (v0 "/\" (v1 "\/" (v2 "/\" v3))) = v0 "/\" (v1 "\/" ((v0 "/\" v2) "/\" v3)) by A388; :: thesis:

end;

A398: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "\/" (v2 "/\" v3))) = v0 "/\" (v1 "\/" (v0 "/\" (v3 "/\" v2)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v3 "/\" v2) = v2 "/\" (v0 "/\" v3) by A14;
hence v0 "/\" (v0 "/\" (v1 "\/" (v2 "/\" v3))) = v0 "/\" (v1 "\/" (v0 "/\" (v3 "/\" v2))) by A391; :: thesis:

end;

A408: for v100, v1 being Element of (BA2TBAA B) holds v100 "/\" (v1 "\/" v100) = v100 "\/" ((v100 "/\" v1) "/\" (v100 "/\" v1))

proof

let v100, v1 be Element of (BA2TBAA B); :: thesis:
(v100 "\/" (v100 "/\" v1)) "/\" (v100 "\/" (v100 "/\" v1)) = v100 "/\" (v1 "\/" v100) by A85;
hence v100 "/\" (v1 "\/" v100) = v100 "\/" ((v100 "/\" v1) "/\" (v100 "/\" v1)) ; :: thesis:

end;

A413: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" v1) = v0 "\/" (v1 "/\" ((v0 "/\" v1) "/\" v0))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "/\" (v0 "/\" v1) = v1 "/\" ((v0 "/\" v1) "/\" v0) by A14;
hence v0 "/\" (v0 "\/" v1) = v0 "\/" (v1 "/\" ((v0 "/\" v1) "/\" v0)) by A408; :: thesis:

end;

A417: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" ((v0 "/\" v1) "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "/\" v1) "/\" v1) = v1 "/\" (v0 "/\" (v0 "/\" v1)) by A14;
hence v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" ((v0 "/\" v1) "/\" v1)) by A413; :: thesis:

end;

A421: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v1) = v1 "/\" (v0 "/\" v1) by A14;
hence v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" v1))) by A417; :: thesis:

end;

A425: for v102, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" v102) = (v0 "\/" (v0 "/\" v1)) "/\" ((v2 "\/" (v0 "/\" v1)) "\/" v102)

proof

let v102, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v2) by A85;
hence (v0 "/\" (v1 "\/" v2)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" v102) = (v0 "\/" (v0 "/\" v1)) "/\" ((v2 "\/" (v0 "/\" v1)) "\/" v102) by A6; :: thesis:

end;

A432: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" ((v0 "/\" v1) "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "\/" ((v0 "/\" v1) "\/" v3) = v3 "\/" (v2 "\/" (v0 "/\" v1)) by A8;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" ((v0 "/\" v1) "\/" v3)) by A425; :: thesis:

end;

A438: for v2, v101, v1, v0 being Element of (BA2TBAA B) holds ((v0 "\/" (v0 "/\" v1)) "/\" v101) "\/" (v0 "/\" (v1 "\/" v2)) = (v0 "\/" (v0 "/\" v1)) "/\" (v101 "\/" (v2 "\/" (v0 "/\" v1)))

proof

let v2, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v2) by A85;
hence ((v0 "\/" (v0 "/\" v1)) "/\" v101) "\/" (v0 "/\" (v1 "\/" v2)) = (v0 "\/" (v0 "/\" v1)) "/\" (v101 "\/" (v2 "\/" (v0 "/\" v1))) by A6; :: thesis:

end;

A444: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v1 "/\" v2))) "\/" (v1 "/\" (v2 "\/" v3)) = (v1 "/\" (v2 "\/" v0)) "\/" (v3 "/\" (v1 "\/" (v1 "/\" v2)))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" (v1 "/\" v2)) "/\" (v0 "\/" (v3 "\/" (v1 "/\" v2))) = (v1 "/\" (v2 "\/" v0)) "\/" (v3 "/\" (v1 "\/" (v1 "/\" v2))) by A432;
hence (v0 "/\" (v1 "\/" (v1 "/\" v2))) "\/" (v1 "/\" (v2 "\/" v3)) = (v1 "/\" (v2 "\/" v0)) "\/" (v3 "/\" (v1 "\/" (v1 "/\" v2))) by A438; :: thesis:

end;

A447: for v100, v101, v2, v1 being Element of (BA2TBAA B) holds (v100 "\/" (v100 "/\" v101)) "/\" ((v1 "\/" v2) "\/" (v100 "/\" v101)) = v100 "/\" (v2 "\/" (v101 "\/" v1))

proof

let v100, v101, v2, v1 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v1 "\/" v2) = v2 "\/" (v101 "\/" v1) by A8;
hence (v100 "\/" (v100 "/\" v101)) "/\" ((v1 "\/" v2) "\/" (v100 "/\" v101)) = v100 "/\" (v2 "\/" (v101 "\/" v1)) by A85; :: thesis:

end;

A450: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1))) = v0 "/\" (v3 "\/" (v1 "\/" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v2 "\/" v3) "\/" (v0 "/\" v1) = v2 "\/" (v3 "\/" (v0 "/\" v1)) by A181;
hence (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1))) = v0 "/\" (v3 "\/" (v1 "\/" v2)) by A447; :: thesis:

end;

A452: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v3 "\/" (v1 "\/" v2))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1))) = (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) by A432;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v3 "\/" (v1 "\/" v2)) by A450; :: thesis:

end;

A454: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v2 "\/" (v3 "\/" v1))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v3 "\/" (v1 "\/" v2) = v2 "\/" (v3 "\/" v1) by A8;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v2 "\/" (v3 "\/" v1)) by A452; :: thesis:

end;

A458: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v3 "\/" v2))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v3 "\/" v2) = v2 "\/" (v1 "\/" v3) by A8;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v3 "\/" v2)) by A454; :: thesis:

end;

A504: for v102, v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" ((v2 "\/" (v0 "/\" v1)) "/\" v102) = (v2 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" v102)

proof

let v102, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v2) by A85;
hence (v0 "/\" (v1 "\/" v2)) "\/" ((v2 "\/" (v0 "/\" v1)) "/\" v102) = (v2 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" v102) by A6; :: thesis:

end;

A511: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v2 "\/" (v0 "/\" v1))) = (v2 "\/" (v0 "/\" v1)) "/\" (v0 "\/" ((v0 "/\" v1) "\/" v3))

proof

let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v1) "\/" v3) = v3 "\/" (v0 "\/" (v0 "/\" v1)) by A8;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v2 "\/" (v0 "/\" v1))) = (v2 "\/" (v0 "/\" v1)) "/\" (v0 "\/" ((v0 "/\" v1) "\/" v3)) by A504; :: thesis:

end;

A516: for v102, v101, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" ((v0 "\/" v1) "/\" v101))) "/\" (v102 "\/" ((v0 "\/" v1) "/\" v101)) = (v0 "\/" v1) "/\" (v101 "\/" v102)

proof

let v102, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" v101) = v0 "\/" (v1 "\/" ((v0 "\/" v1) "/\" v101)) by A181;
hence (v0 "\/" (v1 "\/" ((v0 "\/" v1) "/\" v101))) "/\" (v102 "\/" ((v0 "\/" v1) "/\" v101)) = (v0 "\/" v1) "/\" (v101 "\/" v102) by A85; :: thesis:

end;

A523: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds (v2 "/\" (v0 "\/" v1)) "\/" (v3 "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v2 "\/" v3)

proof

let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) "/\" (v3 "\/" (v2 "/\" (v0 "\/" v1))) = (v2 "/\" (v0 "\/" v1)) "\/" (v3 "/\" (v0 "\/" v1)) by A346;
hence (v2 "/\" (v0 "\/" v1)) "\/" (v3 "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v2 "\/" v3) by A516; :: thesis:

end;

A527: for v103, v100 being Element of (BA2TBAA B) holds v100 "/\" (v100 "/\" (v100 "\/" v103)) = v100 "/\" (v100 "\/" (v103 "/\" (v100 "/\" v100)))

proof

let v103, v100 be Element of (BA2TBAA B); :: thesis:
(v100 "\/" (v100 "/\" v100)) "/\" (v103 "\/" (v100 "/\" v100)) = v100 "/\" (v100 "\/" v103) ;
hence v100 "/\" (v100 "/\" (v100 "\/" v103)) = v100 "/\" (v100 "\/" (v103 "/\" (v100 "/\" v100))) by A82; :: thesis:

end;

A530: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v0)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "/\" v0) = v0 "/\" (v1 "/\" v0) by A14;
hence v0 "/\" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v0))) by A527; :: thesis:

end;

A534: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "/\" (v0 "/\" v1))) = v0 "/\" (v0 "\/" (v0 "/\" v1)) by A378;
hence v0 "/\" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" (v0 "/\" v1)) by A530; :: thesis:

end;

A539: for v102, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" (v100 "\/" v1)) "/\" (v100 "\/" v102) = v100 "\/" ((v100 "/\" (v100 "/\" (v1 "/\" v1))) "/\" v102)

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v100 "/\" (v100 "/\" (v1 "/\" v1))) = v100 "/\" (v100 "\/" v1) by A421;
hence (v100 "/\" (v100 "\/" v1)) "/\" (v100 "\/" v102) = v100 "\/" ((v100 "/\" (v100 "/\" (v1 "/\" v1))) "/\" v102) by A4; :: thesis:

end;

A542: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) = v0 "\/" ((v0 "/\" (v0 "/\" (v1 "/\" v1))) "/\" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) by A292;
hence v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) = v0 "\/" ((v0 "/\" (v0 "/\" (v1 "/\" v1))) "/\" v2) by A539; :: thesis:

end;

A544: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" ((v0 "/\" (v0 "/\" (v1 "/\" v1))) "/\" v2)

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" ((v0 "/\" (v0 "/\" (v1 "/\" v1))) "/\" v2) by A542; :: thesis:

end;

A548: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" (v0 "/\" ((v0 "/\" (v1 "/\" v1)) "/\" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "/\" (v1 "/\" v1)) "/\" v2) = v2 "/\" (v0 "/\" (v0 "/\" (v1 "/\" v1))) by A14;
hence v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" (v0 "/\" ((v0 "/\" (v1 "/\" v1)) "/\" v2)) by A544; :: thesis:

end;

A552: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" (v0 "/\" (v0 "/\" ((v1 "/\" v1) "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "/\" v1) "/\" v2) = v2 "/\" (v0 "/\" (v1 "/\" v1)) by A14;
hence v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" (v0 "/\" (v0 "/\" ((v1 "/\" v1) "/\" v2))) by A548; :: thesis:

end;

A556: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v2 "/\" v1))))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "/\" (v1 "/\" v1) = v1 "/\" (v2 "/\" v1) by A14;
hence v0 "/\" (v0 "\/" (v1 "/\" v2)) = v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v2 "/\" v1)))) by A552; :: thesis:

end;

A576: for v1, v101, v100 being Element of (BA2TBAA B) holds (v100 "\/" v101) "/\" (v101 "/\" (v101 "\/" v1)) = v101 "\/" (v100 "/\" (v101 "/\" (v101 "/\" (v1 "/\" v1))))

proof

let v1, v101, v100 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v101 "/\" (v101 "/\" (v1 "/\" v1))) = v101 "/\" (v101 "\/" v1) by A421;
hence (v100 "\/" v101) "/\" (v101 "/\" (v101 "\/" v1)) = v101 "\/" (v100 "/\" (v101 "/\" (v101 "/\" (v1 "/\" v1)))) by A4; :: thesis:

end;

A579: for v0, v2, v1 being Element of (BA2TBAA B) holds v1 "/\" ((v1 "\/" v2) "/\" (v0 "\/" v1)) = v1 "\/" (v0 "/\" (v1 "/\" (v1 "/\" (v2 "/\" v2))))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" ((v1 "\/" v2) "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v1 "/\" (v1 "\/" v2)) by A14;
hence v1 "/\" ((v1 "\/" v2) "/\" (v0 "\/" v1)) = v1 "\/" (v0 "/\" (v1 "/\" (v1 "/\" (v2 "/\" v2)))) by A576; :: thesis:

end;

A582: for v0, v1, v2 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v2 "/\" v1)) = v0 "\/" (v2 "/\" (v0 "/\" (v0 "/\" (v1 "/\" v1))))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v0)) = v0 "/\" (v0 "\/" (v2 "/\" v1)) by A194;
hence v0 "/\" (v0 "\/" (v2 "/\" v1)) = v0 "\/" (v2 "/\" (v0 "/\" (v0 "/\" (v1 "/\" v1)))) by A579; :: thesis:

end;

A590: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v1 "\/" (v1 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1))) by A398;
hence v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A421; :: thesis:

end;

A592: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v1 "\/" (v1 "/\" v1)) by A378;
hence v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A590; :: thesis:

end;

A693: for v102, v1, v100 being Element of (BA2TBAA B) holds v100 "/\" (((v100 "/\" (v1 "/\" v1)) "\/" v102) "/\" (v100 "/\" (v100 "\/" v1))) = v100 "/\" ((v100 "/\" (v1 "/\" v1)) "\/" (v100 "/\" v102))

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v100 "/\" (v100 "/\" (v1 "/\" v1))) = v100 "/\" (v100 "\/" v1) by A421;
hence v100 "/\" (((v100 "/\" (v1 "/\" v1)) "\/" v102) "/\" (v100 "/\" (v100 "\/" v1))) = v100 "/\" ((v100 "/\" (v1 "/\" v1)) "\/" (v100 "/\" v102)) by A82; :: thesis:

end;

A699: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v2) "/\" ((v1 "\/" (v0 "/\" (v2 "/\" v2))) "/\" v0)) = v0 "/\" ((v0 "/\" (v2 "/\" v2)) "\/" (v0 "/\" v1))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" (v0 "/\" (v2 "/\" v2))) "/\" (v0 "/\" (v0 "\/" v2)) = (v0 "\/" v2) "/\" ((v1 "\/" (v0 "/\" (v2 "/\" v2))) "/\" v0) by A14;
hence v0 "/\" ((v0 "\/" v2) "/\" ((v1 "\/" (v0 "/\" (v2 "/\" v2))) "/\" v0)) = v0 "/\" ((v0 "/\" (v2 "/\" v2)) "\/" (v0 "/\" v1)) by A693; :: thesis:

end;

A704: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v2 "\/" (v0 "/\" (v1 "/\" v1))) "/\" (v0 "\/" v1))) = v0 "/\" ((v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v2 "\/" (v0 "/\" (v1 "/\" v1))) "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) by A14;
hence v0 "/\" (v0 "/\" ((v2 "\/" (v0 "/\" (v1 "/\" v1))) "/\" (v0 "\/" v1))) = v0 "/\" ((v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2)) by A699; :: thesis:

end;

A710: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v0 "/\" ((v1 "/\" v1) "\/" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2) = v0 "/\" ((v1 "/\" v1) "\/" v2) by A6;
hence v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v0 "/\" ((v1 "/\" v1) "\/" v2)) by A704; :: thesis:

end;

A714: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) by A398;
hence v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) by A710; :: thesis:

end;

A717: for v100, v1, v103 being Element of (BA2TBAA B) holds v100 "/\" ((v103 "\/" (v103 "/\" (v1 "/\" v1))) "/\" (v103 "\/" (v100 "/\" v103))) = v100 "/\" (v103 "/\" (v103 "\/" v1))

proof

let v100, v1, v103 be Element of (BA2TBAA B); :: thesis:
v103 "\/" (v103 "/\" (v103 "/\" (v1 "/\" v1))) = v103 "/\" (v103 "\/" v1) by A421;
hence v100 "/\" ((v103 "\/" (v103 "/\" (v1 "/\" v1))) "/\" (v103 "\/" (v100 "/\" v103))) = v100 "/\" (v103 "/\" (v103 "\/" v1)) by A82; :: thesis:

end;

A720: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" ((v1 "/\" (v2 "/\" v2)) "/\" (v0 "/\" v1))) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" (v1 "/\" (v2 "/\" v2))) "/\" (v1 "\/" (v0 "/\" v1)) = v1 "\/" ((v1 "/\" (v2 "/\" v2)) "/\" (v0 "/\" v1)) by A4;
hence v0 "/\" (v1 "\/" ((v1 "/\" (v2 "/\" v2)) "/\" (v0 "/\" v1))) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A717; :: thesis:

end;

A722: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v1 "/\" ((v1 "/\" (v2 "/\" v2)) "/\" v0))) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" (v2 "/\" v2)) "/\" (v0 "/\" v1) = v1 "/\" ((v1 "/\" (v2 "/\" v2)) "/\" v0) by A14;
hence v0 "/\" (v1 "\/" (v1 "/\" ((v1 "/\" (v2 "/\" v2)) "/\" v0))) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A720; :: thesis:

end;

A726: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" ((v1 "/\" (v2 "/\" v2)) "/\" v1))) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "/\" (v2 "/\" v2)) "/\" v1) = v1 "/\" (v0 "/\" (v1 "/\" (v2 "/\" v2))) by A14;
hence v0 "/\" (v1 "\/" (v0 "/\" ((v1 "/\" (v2 "/\" v2)) "/\" v1))) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A722; :: thesis:

end;

A730: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v0 "/\" (v1 "/\" (v1 "/\" (v2 "/\" v2)))) = v1 "/\" (v1 "\/" (v0 "/\" v2)) by A582;
hence v0 "/\" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A726; :: thesis:

end;

A733: for v1, v100 being Element of (BA2TBAA B) holds v100 "\/" (v100 "/\" (v100 "/\" (v1 "\/" (v1 "/\" (v100 "/\" v1))))) = v100 "/\" (v100 "\/" (v1 "\/" (v100 "/\" v1)))

proof

let v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" ((v1 "\/" (v100 "/\" v1)) "/\" (v1 "\/" (v100 "/\" v1))) = v100 "/\" (v1 "\/" (v1 "/\" (v100 "/\" v1))) by A82;
hence v100 "\/" (v100 "/\" (v100 "/\" (v1 "\/" (v1 "/\" (v100 "/\" v1))))) = v100 "/\" (v100 "\/" (v1 "\/" (v100 "/\" v1))) by A421; :: thesis:

end;

A736: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v1) = v1 "/\" (v0 "/\" v1) by A14;
hence v0 "\/" (v0 "/\" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) by A733; :: thesis:

end;

A738: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "/\" (v1 "\/" (v1 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v1 "\/" (v1 "/\" v1)) by A378;
hence v0 "\/" (v0 "/\" (v0 "/\" (v1 "\/" (v1 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) by A736; :: thesis:

end;

A740: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1)))

proof

end;

A742: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1)))

proof

end;

A744: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "\/" v1)) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A592;
hence v0 "/\" (v0 "\/" (v1 "\/" v1)) = v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) by A742; :: thesis:

end;

A754: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "/\" v1) "/\" (v0 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A85;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "/\" v1) "/\" (v0 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A421; :: thesis:

end;

A756: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" ((v0 "/\" v1) "/\" v0)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "/\" (v0 "/\" v1) = v1 "/\" ((v0 "/\" v1) "/\" v0) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" ((v0 "/\" v1) "/\" v0)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A754; :: thesis:

end;

A760: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" ((v0 "/\" v1) "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "/\" v1) "/\" v1) = v1 "/\" (v0 "/\" (v0 "/\" v1)) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" ((v0 "/\" v1) "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A756; :: thesis:

end;

A764: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v1) = v1 "/\" (v0 "/\" v1) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A760; :: thesis:

end;

A766: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" ((v0 "/\" (v1 "/\" v1)) "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "/\" (v1 "/\" v1)) "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" v1))) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" ((v0 "/\" (v1 "/\" v1)) "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A764; :: thesis:

end;

A768: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" ((v1 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v1)) "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" ((v1 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1))) by A292;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" ((v1 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A766; :: thesis:

end;

A770: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1)) = v1 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) by A292;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A768; :: thesis:

end;

A772: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v1 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v1))) by A398;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A770; :: thesis:

end;

A774: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v1) = v1 "/\" (v0 "/\" v1) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A772; :: thesis:

end;

A776: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" ((v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))))) "/\" (v0 "\/" (v0 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))))) "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1)))))) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" ((v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))))) "/\" (v0 "\/" (v0 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A774; :: thesis:

end;

A780: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" ((v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1)))) "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1)))) "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "\/" (v0 "/\" v1)) "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))))) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" ((v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1)))) "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A776; :: thesis:

end;

A784: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" ((v0 "\/" (v0 "/\" (v1 "/\" v1))) "/\" (v0 "\/" (v0 "/\" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" ((v0 "\/" (v0 "/\" (v1 "/\" v1))) "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1)))) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" ((v0 "\/" (v0 "/\" (v1 "/\" v1))) "/\" (v0 "\/" (v0 "/\" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A780; :: thesis:

end;

A788: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" ((v0 "/\" v1) "/\" (v0 "/\" (v1 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "/\" (v1 "/\" v1))) ;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" ((v0 "/\" v1) "/\" (v0 "/\" (v1 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A784; :: thesis:

end;

A790: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" ((v1 "/\" v1) "/\" (v0 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "/\" v1) "/\" (v0 "/\" v1)) = (v0 "/\" v1) "/\" (v0 "/\" (v1 "/\" v1)) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" ((v1 "/\" v1) "/\" (v0 "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A788; :: thesis:

end;

A796: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v0 "/\" ((v1 "/\" v1) "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "/\" v1) "/\" v1) = v1 "/\" (v0 "/\" (v1 "/\" v1)) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" (v0 "/\" ((v1 "/\" v1) "/\" v1))))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A790; :: thesis:

end;

A800: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "/\" (v0 "\/" (v1 "/\" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v1 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "/\" v1)) by A556;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "/\" (v0 "\/" (v1 "/\" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A796; :: thesis:

end;

A802: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "/\" (v0 "\/" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "/\" (v0 "\/" (v1 "/\" v1))) = v1 "/\" (v0 "/\" (v0 "\/" v1)) ;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "/\" (v0 "\/" v1))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A800; :: thesis:

end;

A804: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" v1) = v1 "/\" (v0 "/\" (v0 "\/" v1)) by A14;
hence (v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A802; :: thesis:

end;

A808: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" ((v0 "/\" v1) "\/" (v0 "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1))))) = v0 "\/" ((v0 "/\" v1) "\/" (v0 "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) by A181;
hence v0 "\/" ((v0 "/\" v1) "\/" (v0 "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A804; :: thesis:

end;

A810: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1))))) = v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1))))) by A6;
hence v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v1 "\/" (v0 "\/" (v0 "/\" v1))) by A808; :: thesis:

end;

A812: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v0 "\/" ((v0 "/\" v1) "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v1) "\/" v1) = v1 "\/" (v0 "\/" (v0 "/\" v1)) by A8;
hence v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v0 "\/" ((v0 "/\" v1) "\/" v1)) by A810; :: thesis:

end;

A816: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A744;
hence v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1)))))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A812; :: thesis:

end;

A821: for v102, v1, v100 being Element of (BA2TBAA B) holds v100 "/\" ((v100 "/\" (v100 "\/" v1)) "/\" v102) = v102 "/\" (v100 "/\" (v100 "\/" (v100 "/\" v1)))

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "/\" (v100 "\/" v1)) = v100 "/\" (v100 "\/" (v100 "/\" v1)) by A534;
hence v100 "/\" ((v100 "/\" (v100 "\/" v1)) "/\" v102) = v102 "/\" (v100 "/\" (v100 "\/" (v100 "/\" v1))) by A14; :: thesis:

end;

A827: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v0 "\/" v2) "/\" v1)) = v1 "/\" (v0 "/\" (v0 "\/" (v0 "/\" v2)))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v2) "/\" v1) = v1 "/\" (v0 "/\" (v0 "\/" v2)) by A14;
hence v0 "/\" (v0 "/\" ((v0 "\/" v2) "/\" v1)) = v1 "/\" (v0 "/\" (v0 "\/" (v0 "/\" v2))) by A821; :: thesis:

end;

A833: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v2))) = v0 "/\" ((v0 "\/" (v0 "/\" v2)) "/\" v1)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" (v0 "/\" v2)) "/\" v1) = v1 "/\" (v0 "/\" (v0 "\/" (v0 "/\" v2))) by A14;
hence v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v2))) = v0 "/\" ((v0 "\/" (v0 "/\" v2)) "/\" v1) by A827; :: thesis:

end;

A839: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A534; :: thesis:

end;

A841: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v2 "\/" ((v0 "\/" v1) "\/" v1))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v1 "\/" v2) = v2 "\/" ((v0 "\/" v1) "\/" v1) by A8;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v2 "\/" ((v0 "\/" v1) "\/" v1))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A839; :: thesis:

end;

A845: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "\/" (v1 "\/" v1)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "\/" v1) = v1 "\/" (v0 "\/" v1) by A8;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "\/" (v1 "\/" v1)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A841; :: thesis:

end;

A847: for v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" v1) "\/" v2))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "\/" v1) "\/" v2) = v2 "\/" (v0 "\/" (v1 "\/" v1)) by A8;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" v1) "\/" v2))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A845; :: thesis:

end;

A851: for v0, v1, v2 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v2 "\/" v1)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v2 "\/" (v1 "\/" v1) = v1 "\/" (v2 "\/" v1) by A8;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v2 "\/" v1)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A847; :: thesis:

end;

A855: for v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v1 "\/" v2))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2))) by A4;
hence (v0 "\/" v1) "/\" (v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A851; :: thesis:

end;

A857: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "/\" (v1 "\/" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2)))) = v0 "\/" (v1 "/\" (v1 "/\" (v1 "\/" (v1 "\/" v2)))) by A4;
hence v0 "\/" (v1 "/\" (v1 "/\" (v1 "\/" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A855; :: thesis:

end;

A859: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v1 "/\" (v1 "\/" (v1 "\/" v2))) = v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2))) by A534;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) by A857; :: thesis:

end;

A861: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v1 "\/" ((v0 "/\" v2) "\/" (v0 "\/" v1)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" ((v0 "/\" v2) "\/" (v0 "\/" v1)) = (v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v1 "\/" ((v0 "/\" v2) "\/" (v0 "\/" v1))) by A859; :: thesis:

end;

A863: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v1 "\/" (v1 "\/" ((v0 "/\" v2) "\/" v0)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v2) "\/" (v0 "\/" v1) = v1 "\/" ((v0 "/\" v2) "\/" v0) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v1 "\/" (v1 "\/" ((v0 "/\" v2) "\/" v0))) by A861; :: thesis:

end;

A867: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v1 "\/" (v0 "\/" ((v0 "/\" v2) "\/" v1)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v2) "\/" v1) = v1 "\/" (v0 "\/" (v0 "/\" v2)) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v1 "\/" (v0 "\/" ((v0 "/\" v2) "\/" v1))) by A863; :: thesis:

end;

A871: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" (v0 "/\" v2)) "\/" v1))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "\/" (v0 "/\" v2)) "\/" v1) = v1 "\/" (v0 "\/" (v1 "\/" (v0 "/\" v2))) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = (v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" (v0 "/\" v2)) "\/" v1)) by A867; :: thesis:

end;

A875: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2))))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) by A4;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) by A871; :: thesis:

end;

A879: for v102, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" (v100 "\/" (v100 "/\" v1))) "\/" ((v100 "/\" (v100 "\/" v1)) "/\" v102) = (v100 "/\" (v100 "\/" v1)) "/\" (v100 "\/" v102)

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "/\" (v100 "\/" v1)) = v100 "/\" (v100 "\/" (v100 "/\" v1)) by A534;
hence (v100 "/\" (v100 "\/" (v100 "/\" v1))) "\/" ((v100 "/\" (v100 "\/" v1)) "/\" v102) = (v100 "/\" (v100 "\/" v1)) "/\" (v100 "\/" v102) by A6; :: thesis:

end;

A884: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v0 "\/" (v0 "/\" v1))) "\/" (v0 "/\" ((v0 "\/" v1) "/\" v2)) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" v2) = v2 "/\" (v0 "/\" (v0 "\/" v1)) by A14;
hence (v0 "/\" (v0 "\/" (v0 "/\" v1))) "\/" (v0 "/\" ((v0 "\/" v1) "/\" v2)) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A879; :: thesis:

end;

A888: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v2 "/\" (v0 "\/" v1))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" (v0 "/\" v1))) "\/" (v0 "/\" (v2 "/\" (v0 "\/" v1))) = v0 "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v2 "/\" (v0 "\/" v1))) by A6;
hence v0 "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v2 "/\" (v0 "\/" v1))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A884; :: thesis:

end;

A890: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" ((v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v1)))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "\/" (v2 "/\" (v0 "\/" v1)) = v0 "\/" ((v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v1))) by A181;
hence v0 "/\" (v0 "\/" ((v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v1)))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A888; :: thesis:

end;

A892: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" v2))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v1))) = v0 "\/" (v1 "/\" (v0 "\/" v2)) by A261;
hence v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" v2))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A890; :: thesis:

end;

A894: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" v2))) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) by A292;
hence v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" v2))) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) by A892; :: thesis:

end;

A896: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" v2))) = v0 "/\" (v0 "\/" (v1 "/\" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" v2))) = v0 "/\" (v0 "\/" (v1 "/\" v2)) by A894; :: thesis:

end;

A907: for v102, v103, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" (v100 "\/" (v100 "/\" v1))) "/\" (v102 "\/" v103) = v100 "/\" ((v100 "/\" (v100 "\/" v1)) "/\" (v102 "\/" v103))

proof

let v102, v103, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "/\" (v100 "\/" v1)) = v100 "/\" (v100 "\/" (v100 "/\" v1)) by A534;
hence (v100 "/\" (v100 "\/" (v100 "/\" v1))) "/\" (v102 "\/" v103) = v100 "/\" ((v100 "/\" (v100 "\/" v1)) "/\" (v102 "\/" v103)) by A292; :: thesis:

end;

A910: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) = v0 "/\" ((v0 "/\" (v0 "\/" v1)) "/\" (v2 "\/" v3))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" (v0 "/\" v1))) "/\" (v2 "\/" v3) = v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) by A292;
hence v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) = v0 "/\" ((v0 "/\" (v0 "\/" v1)) "/\" (v2 "\/" v3)) by A907; :: thesis:

end;

A912: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) = v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "/\" (v2 "\/" v3) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)) by A292;
hence v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) = v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3))) by A910; :: thesis:

end;

A932: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" v2)))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v1 "\/" (v1 "/\" (v1 "\/" v2))) = v1 "/\" (v1 "\/" (v1 "/\" v2)) by A896;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "/\" v2))) by A875; :: thesis:

end;

A941: for v102, v100, v101, v1 being Element of (BA2TBAA B) holds v100 "\/" ((v101 "/\" v102) "\/" (v100 "\/" (v1 "/\" v101))) = v100 "\/" (v101 "/\" ((v100 "\/" v1) "\/" v102))

proof

let v102, v100, v101, v1 be Element of (BA2TBAA B); :: thesis:
(v100 "\/" v1) "/\" (v100 "\/" v101) = v100 "\/" (v1 "/\" v101) by A4;
hence v100 "\/" ((v101 "/\" v102) "\/" (v100 "\/" (v1 "/\" v101))) = v100 "\/" (v101 "/\" ((v100 "\/" v1) "\/" v102)) by A106; :: thesis:

end;

A946: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" ((v1 "/\" v3) "\/" (v1 "/\" v2))) = v0 "\/" (v1 "/\" ((v0 "\/" v3) "\/" v2))

proof

let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "/\" v3) "\/" (v1 "/\" v2)) = (v1 "/\" v2) "\/" (v0 "\/" (v1 "/\" v3)) by A8;
hence v0 "\/" (v0 "\/" ((v1 "/\" v3) "\/" (v1 "/\" v2))) = v0 "\/" (v1 "/\" ((v0 "\/" v3) "\/" v2)) by A941; :: thesis:

end;

A949: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" v3))) = v0 "\/" (v1 "/\" ((v0 "\/" v2) "\/" v3))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v2) "\/" (v1 "/\" v3) = v1 "/\" (v2 "\/" v3) by A6;
hence v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" v3))) = v0 "\/" (v1 "/\" ((v0 "\/" v2) "\/" v3)) by A946; :: thesis:

end;

A956: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" v3))) = v0 "\/" (v1 "/\" (v0 "\/" (v3 "\/" v2)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v3 "\/" v2) = v2 "\/" (v0 "\/" v3) by A8;
hence v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" v3))) = v0 "\/" (v1 "/\" (v0 "\/" (v3 "\/" v2))) by A949; :: thesis:

end;

A982: for v103, v100, v1, v101 being Element of (BA2TBAA B) holds (v100 "/\" (v101 "/\" (v101 "\/" (v101 "/\" v1)))) "\/" ((v101 "/\" (v101 "\/" v1)) "/\" v103) = (v101 "/\" (v101 "\/" v1)) "/\" (v103 "\/" (v100 "/\" v101))

proof

let v103, v100, v1, v101 be Element of (BA2TBAA B); :: thesis:
v101 "/\" (v101 "/\" (v101 "\/" v1)) = v101 "/\" (v101 "\/" (v101 "/\" v1)) by A534;
hence (v100 "/\" (v101 "/\" (v101 "\/" (v101 "/\" v1)))) "\/" ((v101 "/\" (v101 "\/" v1)) "/\" v103) = (v101 "/\" (v101 "\/" v1)) "/\" (v103 "\/" (v100 "/\" v101)) by A131; :: thesis:

end;

A987: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" (v1 "\/" (v1 "/\" v2)))) "\/" (v1 "/\" ((v1 "\/" v2) "/\" v3)) = (v1 "/\" (v1 "\/" v2)) "/\" (v3 "\/" (v0 "/\" v1))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" ((v1 "\/" v2) "/\" v3) = v3 "/\" (v1 "/\" (v1 "\/" v2)) by A14;
hence (v0 "/\" (v1 "/\" (v1 "\/" (v1 "/\" v2)))) "\/" (v1 "/\" ((v1 "\/" v2) "/\" v3)) = (v1 "/\" (v1 "\/" v2)) "/\" (v3 "\/" (v0 "/\" v1)) by A982; :: thesis:

end;

A991: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v1 "/\" ((v3 "/\" (v1 "\/" v2)) "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = (v1 "/\" (v1 "\/" v2)) "/\" (v3 "\/" (v0 "/\" v1))

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" (v1 "\/" (v1 "/\" v2)))) "\/" (v1 "/\" (v3 "/\" (v1 "\/" v2))) = v1 "/\" ((v3 "/\" (v1 "\/" v2)) "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) by A123;
hence v1 "/\" ((v3 "/\" (v1 "\/" v2)) "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = (v1 "/\" (v1 "\/" v2)) "/\" (v3 "\/" (v0 "/\" v1)) by A987; :: thesis:

end;

A994: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2)))) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0)))

proof

let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v2)) "/\" (v1 "\/" (v3 "/\" v0)) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0))) by A292;
hence v0 "/\" ((v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2)))) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0))) by A991; :: thesis:

end;

A1005: for v100, v3, v101 being Element of (BA2TBAA B) holds v100 "/\" (v101 "\/" (v101 "/\" v3)) = v101 "/\" (v100 "\/" (v100 "/\" v3))

proof

let v100, v3, v101 be Element of (BA2TBAA B); :: thesis:
(v100 "/\" v101) "\/" (v101 "/\" (v100 "/\" v3)) = v100 "/\" (v101 "\/" (v101 "/\" v3)) by A159;
hence v100 "/\" (v101 "\/" (v101 "/\" v3)) = v101 "/\" (v100 "\/" (v100 "/\" v3)) by A6; :: thesis:

end;

A1020: for v2, v101, v100 being Element of (BA2TBAA B) holds v100 "/\" ((v100 "\/" v101) "\/" ((v100 "\/" v101) "/\" v2)) = v100 "\/" (v101 "/\" (v100 "/\" v2))

proof

let v2, v101, v100 be Element of (BA2TBAA B); :: thesis:
(v100 "\/" v101) "/\" (v100 "\/" (v100 "/\" v2)) = v100 "/\" ((v100 "\/" v101) "\/" ((v100 "\/" v101) "/\" v2)) by A1005;
hence v100 "/\" ((v100 "\/" v101) "\/" ((v100 "\/" v101) "/\" v2)) = v100 "\/" (v101 "/\" (v100 "/\" v2)) by A4; :: thesis:

end;

A1025: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = v0 "\/" (v1 "/\" (v0 "/\" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v2 "/\" (v0 "\/" v1)) = v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1))) by A181;
hence v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = v0 "\/" (v1 "/\" (v0 "/\" v2)) by A1020; :: thesis:

end;

A1027: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = v0 "\/" (v0 "/\" (v2 "/\" v1))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v1) = v1 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = v0 "\/" (v0 "/\" (v2 "/\" v1)) by A1025; :: thesis:

end;

A1032: for v100, v102, v101 being Element of (BA2TBAA B) holds v100 "/\" (v100 "/\" ((v101 "\/" v102) "\/" ((v101 "\/" v102) "/\" v101))) = v100 "/\" (v101 "\/" (v100 "/\" v102))

proof

let v100, v102, v101 be Element of (BA2TBAA B); :: thesis:
(v101 "\/" v102) "/\" (v100 "\/" (v100 "/\" v101)) = v100 "/\" ((v101 "\/" v102) "\/" ((v101 "\/" v102) "/\" v101)) by A1005;
hence v100 "/\" (v100 "/\" ((v101 "\/" v102) "\/" ((v101 "\/" v102) "/\" v101))) = v100 "/\" (v101 "\/" (v100 "/\" v102)) by A82; :: thesis:

end;

A1037: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" (v1 "\/" v2))))) = v0 "/\" (v1 "\/" (v0 "/\" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v2) "\/" (v1 "/\" (v1 "\/" v2)) = v1 "\/" (v2 "\/" (v1 "/\" (v1 "\/" v2))) by A181;
hence v0 "/\" (v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" (v1 "\/" v2))))) = v0 "/\" (v1 "\/" (v0 "/\" v2)) by A1032; :: thesis:

end;

A1040: for v101, v100 being Element of (BA2TBAA B) holds v100 "/\" ((v100 "\/" (v100 "/\" v101)) "\/" ((v100 "\/" (v100 "/\" v101)) "/\" v101)) = v100 "/\" (v101 "\/" v100)

proof

let v101, v100 be Element of (BA2TBAA B); :: thesis:
(v100 "\/" (v100 "/\" v101)) "/\" (v100 "\/" (v100 "/\" v101)) = v100 "/\" ((v100 "\/" (v100 "/\" v101)) "\/" ((v100 "\/" (v100 "/\" v101)) "/\" v101)) by A1005;
hence v100 "/\" ((v100 "\/" (v100 "/\" v101)) "\/" ((v100 "\/" (v100 "/\" v101)) "/\" v101)) = v100 "/\" (v101 "\/" v100) by A85; :: thesis:

end;

A1045: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" ((v0 "/\" v1) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "\/" ((v0 "/\" v1) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))) by A181;
hence v0 "/\" (v0 "\/" ((v0 "/\" v1) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" v0) by A1040; :: thesis:

end;

A1047: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v1 "/\" (v0 "\/" (v0 "\/" (v0 "/\" v1))) by A6;
hence v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" v0) by A1045; :: thesis:

end;

A1049: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v0 "\/" (v0 "\/" (v0 "/\" v1)))) = v0 "\/" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))) by A956;
hence v0 "/\" (v0 "\/" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))))) = v0 "/\" (v1 "\/" v0) by A1047; :: thesis:

end;

A1054: for v100, v2, v1 being Element of (BA2TBAA B) holds v100 "/\" (v100 "/\" (v100 "\/" (v1 "\/" (v1 "/\" v2)))) = v100 "/\" (v100 "\/" (v1 "/\" (v100 "\/" (v100 "/\" v2))))

proof

let v100, v2, v1 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v1 "\/" (v1 "/\" v2)) = v1 "/\" (v100 "\/" (v100 "/\" v2)) by A1005;
hence v100 "/\" (v100 "/\" (v100 "\/" (v1 "\/" (v1 "/\" v2)))) = v100 "/\" (v100 "\/" (v1 "/\" (v100 "\/" (v100 "/\" v2)))) by A534; :: thesis:

end;

A1057: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v2))))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) by A534;
hence v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v2)))) by A1054; :: thesis:

end;

A1059: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v2)))) = v0 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v2))) by A896;
hence v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v2))) by A1057; :: thesis:

end;

A1061: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v0 "/\" (v2 "/\" v1)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v1) = v1 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v0 "/\" (v2 "/\" v1))) by A1059; :: thesis:

end;

A1066: for v103, v102, v2, v100 being Element of (BA2TBAA B) holds v100 "\/" (((v100 "/\" v2) "/\" v102) "\/" (v100 "/\" (v103 "\/" (v103 "/\" v2)))) = v100 "\/" ((v100 "/\" v2) "/\" (v103 "\/" v102))

proof

let v103, v102, v2, v100 be Element of (BA2TBAA B); :: thesis:
v103 "/\" (v100 "\/" (v100 "/\" v2)) = v100 "/\" (v103 "\/" (v103 "/\" v2)) by A1005;
hence v100 "\/" (((v100 "/\" v2) "/\" v102) "\/" (v100 "/\" (v103 "\/" (v103 "/\" v2)))) = v100 "\/" ((v100 "/\" v2) "/\" (v103 "\/" v102)) by A106; :: thesis:

end;

A1072: for v3, v2, v0, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v2 "/\" (v1 "/\" v0)) "\/" (v0 "/\" (v3 "\/" (v3 "/\" v2)))) = v0 "\/" ((v0 "/\" v2) "/\" (v3 "\/" v1))

proof

let v3, v2, v0, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "/\" v2) = v2 "/\" (v1 "/\" v0) by A14;
hence v0 "\/" ((v2 "/\" (v1 "/\" v0)) "\/" (v0 "/\" (v3 "\/" (v3 "/\" v2)))) = v0 "\/" ((v0 "/\" v2) "/\" (v3 "\/" v1)) by A1066; :: thesis:

end;

A1077: for v3, v0, v1, v2 being Element of (BA2TBAA B) holds v0 "\/" ((v0 "/\" (v2 "/\" v1)) "\/" (v0 "/\" (v3 "\/" (v3 "/\" v1)))) = v0 "\/" ((v0 "/\" v1) "/\" (v3 "\/" v2))

proof

let v3, v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v1) = v1 "/\" (v0 "/\" v2) by A14;
hence v0 "\/" ((v0 "/\" (v2 "/\" v1)) "\/" (v0 "/\" (v3 "\/" (v3 "/\" v1)))) = v0 "\/" ((v0 "/\" v1) "/\" (v3 "\/" v2)) by A1072; :: thesis:

end;

A1085: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" ((v1 "/\" v2) "\/" (v3 "\/" (v1 "/\" v3)))) = v0 "\/" ((v0 "/\" v1) "/\" (v3 "\/" v2))

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v2)) "\/" (v0 "/\" (v3 "\/" (v1 "/\" v3))) = v0 "/\" ((v1 "/\" v2) "\/" (v3 "\/" (v1 "/\" v3))) by A6;
hence v0 "\/" (v0 "/\" ((v1 "/\" v2) "\/" (v3 "\/" (v1 "/\" v3)))) = v0 "\/" ((v0 "/\" v1) "/\" (v3 "\/" v2)) by A1077; :: thesis:

end;

A1087: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v3 "\/" ((v1 "/\" v3) "\/" (v1 "/\" v2)))) = v0 "\/" ((v0 "/\" v1) "/\" (v3 "\/" v2))

proof

let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis:
v3 "\/" ((v1 "/\" v3) "\/" (v1 "/\" v2)) = (v1 "/\" v2) "\/" (v3 "\/" (v1 "/\" v3)) by A8;
hence v0 "\/" (v0 "/\" (v3 "\/" ((v1 "/\" v3) "\/" (v1 "/\" v2)))) = v0 "\/" ((v0 "/\" v1) "/\" (v3 "\/" v2)) by A1085; :: thesis:

end;

A1090: for v0, v2, v3, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v2 "/\" (v1 "\/" v3)))) = v0 "\/" ((v0 "/\" v2) "/\" (v1 "\/" v3))

proof

let v0, v2, v3, v1 be Element of (BA2TBAA B); :: thesis:
(v2 "/\" v1) "\/" (v2 "/\" v3) = v2 "/\" (v1 "\/" v3) by A6;
hence v0 "\/" (v0 "/\" (v1 "\/" (v2 "/\" (v1 "\/" v3)))) = v0 "\/" ((v0 "/\" v2) "/\" (v1 "\/" v3)) by A1087; :: thesis:

end;

A1096: for v0, v2, v1, v3 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v2 "/\" (v3 "\/" v1)))) = v0 "\/" (v0 "/\" (v2 "/\" (v3 "\/" v1)))

proof

let v0, v2, v1, v3 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v2) "/\" (v3 "\/" v1) = v0 "/\" (v2 "/\" (v3 "\/" v1)) by A292;
hence v0 "\/" (v0 "/\" (v1 "\/" (v2 "/\" (v3 "\/" v1)))) = v0 "\/" (v0 "/\" (v2 "/\" (v3 "\/" v1))) by A1090; :: thesis:

end;

A1099: for v100, v101, v2, v103 being Element of (BA2TBAA B) holds v100 "\/" ((v101 "/\" (v103 "/\" v2)) "\/" (v103 "/\" (v100 "\/" v101))) = v100 "\/" (v103 "/\" (v101 "\/" (v101 "/\" v2)))

proof

let v100, v101, v2, v103 be Element of (BA2TBAA B); :: thesis:
v101 "/\" (v103 "\/" (v103 "/\" v2)) = v103 "/\" (v101 "\/" (v101 "/\" v2)) by A1005;
hence v100 "\/" ((v101 "/\" (v103 "/\" v2)) "\/" (v103 "/\" (v100 "\/" v101))) = v100 "\/" (v103 "/\" (v101 "\/" (v101 "/\" v2))) by A106; :: thesis:

end;

A1102: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v2 "/\" ((v0 "\/" v1) "\/" (v1 "/\" v3))) = v0 "\/" (v2 "/\" (v1 "\/" (v1 "/\" v3)))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" (v2 "/\" v3)) "\/" (v2 "/\" (v0 "\/" v1)) = v2 "/\" ((v0 "\/" v1) "\/" (v1 "/\" v3)) by A123;
hence v0 "\/" (v2 "/\" ((v0 "\/" v1) "\/" (v1 "/\" v3))) = v0 "\/" (v2 "/\" (v1 "\/" (v1 "/\" v3))) by A1099; :: thesis:

end;

A1105: for v1, v0, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v0 "\/" (v2 "\/" (v2 "/\" v3)))) = v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3)))

proof

let v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v2) "\/" (v2 "/\" v3) = v0 "\/" (v2 "\/" (v2 "/\" v3)) by A181;
hence v0 "\/" (v1 "/\" (v0 "\/" (v2 "\/" (v2 "/\" v3)))) = v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3))) by A1102; :: thesis:

end;

A1107: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3)))) = v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v0 "\/" (v2 "\/" (v2 "/\" v3)))) = v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3)))) by A956;
hence v0 "\/" (v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3)))) = v0 "\/" (v1 "/\" (v2 "\/" (v2 "/\" v3))) by A1105; :: thesis:

end;

A1109: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))) by A1107;
hence v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))) = v0 "/\" (v0 "\/" v1) by A1049; :: thesis:

end;

A1111: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v1))) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))) = v0 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v1))) by A896;
hence v0 "/\" (v0 "\/" (v1 "/\" (v0 "/\" v1))) = v0 "/\" (v0 "\/" v1) by A1109; :: thesis:

end;

A1113: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v1) = v1 "/\" (v0 "/\" v1) by A14;
hence v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v0 "\/" v1) by A1111; :: thesis:

end;

A1115: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v0 "/\" v1)) ;
hence v0 "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" (v0 "\/" v1) by A1113; :: thesis:

end;

A1117: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2))) = v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) = v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2))) by A1115;
hence v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2))) = v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v2))) by A1061; :: thesis:

end;

A1119: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2))) = v0 "/\" (v0 "\/" (v1 "/\" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "/\" (v1 "/\" v2))) = v0 "/\" (v0 "\/" (v1 "/\" v2)) by A1115;
hence v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2))) = v0 "/\" (v0 "\/" (v1 "/\" v2)) by A1117; :: thesis:

end;

A1121: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v1 "\/" (v1 "/\" v2)) = v1 "/\" (v1 "\/" v2) by A1115;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" v2)) by A932; :: thesis:

end;

A1126: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" (v0 "\/" v1) by A1115;
hence v0 "/\" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" v1) by A534; :: thesis:

end;

A1159: for v102, v1, v100 being Element of (BA2TBAA B) holds v100 "/\" ((v100 "\/" (v100 "/\" v1)) "/\" v102) = v102 "/\" (v100 "/\" (v100 "\/" v1))

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "\/" (v100 "/\" v1)) = v100 "/\" (v100 "\/" v1) by A1115;
hence v100 "/\" ((v100 "\/" (v100 "/\" v1)) "/\" v102) = v102 "/\" (v100 "/\" (v100 "\/" v1)) by A14; :: thesis:

end;

A1165: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" ((v0 "\/" v2) "/\" v1)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v2) "/\" v1) = v1 "/\" (v0 "/\" (v0 "\/" v2)) by A14;
hence v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" ((v0 "\/" v2) "/\" v1) by A1159; :: thesis:

end;

A1170: for v101, v1, v100 being Element of (BA2TBAA B) holds (v100 "\/" v101) "/\" (v101 "\/" (v100 "\/" (v100 "/\" v1))) = v101 "\/" (v100 "/\" (v100 "\/" v1))

proof

let v101, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "\/" (v100 "/\" v1)) = v100 "/\" (v100 "\/" v1) by A1115;
hence (v100 "\/" v101) "/\" (v101 "\/" (v100 "\/" (v100 "/\" v1))) = v101 "\/" (v100 "/\" (v100 "\/" v1)) by A4; :: thesis:

end;

A1173: for v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" ((v0 "/\" v2) "\/" v1)) = v1 "\/" (v0 "/\" (v0 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v2) "\/" v1) = v1 "\/" (v0 "\/" (v0 "/\" v2)) by A8;
hence (v0 "\/" v1) "/\" (v0 "\/" ((v0 "/\" v2) "\/" v1)) = v1 "\/" (v0 "/\" (v0 "\/" v2)) by A1170; :: thesis:

end;

A1177: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v1 "\/" (v0 "/\" (v0 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v0 "/\" v2))) = v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) by A4;
hence v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v1 "\/" (v0 "/\" (v0 "\/" v2)) by A1173; :: thesis:

end;

A1180: for v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1115; :: thesis:

end;

A1182: for v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v1 "\/" ((v0 "/\" v2) "\/" (v0 "\/" v1))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v1 "\/" ((v0 "/\" v2) "\/" (v0 "\/" v1)) = (v0 "\/" v1) "\/" (v1 "\/" (v0 "/\" v2)) by A8;
hence (v0 "\/" v1) "/\" (v1 "\/" ((v0 "/\" v2) "\/" (v0 "\/" v1))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1180; :: thesis:

end;

A1184: for v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v1 "\/" (v1 "\/" ((v0 "/\" v2) "\/" v0))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v2) "\/" (v0 "\/" v1) = v1 "\/" ((v0 "/\" v2) "\/" v0) by A8;
hence (v0 "\/" v1) "/\" (v1 "\/" (v1 "\/" ((v0 "/\" v2) "\/" v0))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1182; :: thesis:

end;

A1188: for v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v1 "\/" (v0 "\/" ((v0 "/\" v2) "\/" v1))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v2) "\/" v1) = v1 "\/" (v0 "\/" (v0 "/\" v2)) by A8;
hence (v0 "\/" v1) "/\" (v1 "\/" (v0 "\/" ((v0 "/\" v2) "\/" v1))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1184; :: thesis:

end;

A1192: for v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" (v0 "/\" v2)) "\/" v1)) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "\/" (v0 "/\" v2)) "\/" v1) = v1 "\/" (v0 "\/" (v1 "\/" (v0 "/\" v2))) by A8;
hence (v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" (v0 "/\" v2)) "\/" v1)) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1188; :: thesis:

end;

A1196: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) by A4;
hence v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1192; :: thesis:

end;

A1198: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" v2)) by A1121;
hence v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v1 "\/" v2)) by A1196; :: thesis:

end;

A1200: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v2 "\/" ((v0 "\/" v1) "\/" v1))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v1 "\/" v2) = v2 "\/" ((v0 "\/" v1) "\/" v1) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v2 "\/" ((v0 "\/" v1) "\/" v1)) by A1198; :: thesis:

end;

A1204: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v2 "\/" (v0 "\/" (v1 "\/" v1)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "\/" v1) = v1 "\/" (v0 "\/" v1) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v2 "\/" (v0 "\/" (v1 "\/" v1))) by A1200; :: thesis:

end;

A1206: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" v1) "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "\/" v1) "\/" v2) = v2 "\/" (v0 "\/" (v1 "\/" v1)) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v0 "\/" ((v1 "\/" v1) "\/" v2)) by A1204; :: thesis:

end;

A1210: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v2 "\/" v1)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "\/" (v1 "\/" v1) = v1 "\/" (v2 "\/" v1) by A8;
hence v0 "\/" (v1 "/\" (v1 "\/" v2)) = (v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v2 "\/" v1))) by A1206; :: thesis:

end;

A1214: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" v2)) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v1 "\/" v2))) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2))) by A4;
hence v0 "\/" (v1 "/\" (v1 "\/" v2)) = v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" v2))) by A1210; :: thesis:

end;

A1267: for v102, v103, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" (v100 "\/" v1)) "/\" (v102 "\/" v103) = v100 "/\" ((v100 "\/" (v100 "/\" v1)) "/\" (v102 "\/" v103))

proof

let v102, v103, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "\/" (v100 "/\" v1)) = v100 "/\" (v100 "\/" v1) by A1115;
hence (v100 "/\" (v100 "\/" v1)) "/\" (v102 "\/" v103) = v100 "/\" ((v100 "\/" (v100 "/\" v1)) "/\" (v102 "\/" v103)) by A292; :: thesis:

end;

A1270: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)) = v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "/\" (v2 "\/" v3) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)) by A292;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)) = v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) by A1267; :: thesis:

end;

A1272: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)) = v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" v3)) = v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3))) by A912;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3)) = v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v3))) by A1270; :: thesis:

end;

A1377: for v102, v1, v100 being Element of (BA2TBAA B) holds v100 "\/" (((v100 "/\" v1) "/\" v102) "\/" (v100 "/\" (v100 "\/" v1))) = v100 "\/" ((v100 "/\" v1) "/\" (v100 "\/" v102))

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "\/" (v100 "/\" v1)) = v100 "/\" (v100 "\/" v1) by A1115;
hence v100 "\/" (((v100 "/\" v1) "/\" v102) "\/" (v100 "/\" (v100 "\/" v1))) = v100 "\/" ((v100 "/\" v1) "/\" (v100 "\/" v102)) by A106; :: thesis:

end;

A1383: for v2, v0, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v2 "/\" (v1 "/\" v0)) "\/" (v0 "/\" (v0 "\/" v2))) = v0 "\/" ((v0 "/\" v2) "/\" (v0 "\/" v1))

proof

let v2, v0, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "/\" v2) = v2 "/\" (v1 "/\" v0) by A14;
hence v0 "\/" ((v2 "/\" (v1 "/\" v0)) "\/" (v0 "/\" (v0 "\/" v2))) = v0 "\/" ((v0 "/\" v2) "/\" (v0 "\/" v1)) by A1377; :: thesis:

end;

A1388: for v0, v1, v2 being Element of (BA2TBAA B) holds v0 "\/" ((v0 "/\" (v2 "/\" v1)) "\/" (v0 "/\" (v0 "\/" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v1) = v1 "/\" (v0 "/\" v2) by A14;
hence v0 "\/" ((v0 "/\" (v2 "/\" v1)) "\/" (v0 "/\" (v0 "\/" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2)) by A1383; :: thesis:

end;

A1394: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" ((v1 "/\" v2) "\/" (v0 "\/" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v2)) "\/" (v0 "/\" (v0 "\/" v1)) = v0 "/\" ((v1 "/\" v2) "\/" (v0 "\/" v1)) by A6;
hence v0 "\/" (v0 "/\" ((v1 "/\" v2) "\/" (v0 "\/" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2)) by A1388; :: thesis:

end;

A1396: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" ((v1 "/\" v2) "\/" v0))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v2) "\/" (v0 "\/" v1) = v1 "\/" ((v1 "/\" v2) "\/" v0) by A8;
hence v0 "\/" (v0 "/\" (v1 "\/" ((v1 "/\" v2) "\/" v0))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2)) by A1394; :: thesis:

end;

A1400: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" ((v1 "/\" v2) "\/" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "/\" v2) "\/" v1) = v1 "\/" (v0 "\/" (v1 "/\" v2)) by A8;
hence v0 "\/" (v0 "/\" (v0 "\/" ((v1 "/\" v2) "\/" v1))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2)) by A1396; :: thesis:

end;

A1404: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v2))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v2))) = v0 "/\" (v0 "\/" (v1 "/\" v2)) by A1119;
hence v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v2))) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "\/" v2)) by A1400; :: thesis:

end;

A1406: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v2))) = v0 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v2)))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "/\" (v0 "\/" v2) = v0 "/\" (v1 "/\" (v0 "\/" v2)) by A292;
hence v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v2))) = v0 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v2))) by A1404; :: thesis:

end;

A1410: for v103, v100, v1, v101 being Element of (BA2TBAA B) holds (v100 "/\" (v101 "/\" (v101 "\/" v1))) "\/" (v101 "/\" v103) = v101 "/\" (v103 "\/" (v100 "/\" (v101 "\/" (v101 "/\" v1))))

proof

let v103, v100, v1, v101 be Element of (BA2TBAA B); :: thesis:
v101 "/\" (v101 "\/" (v101 "/\" v1)) = v101 "/\" (v101 "\/" v1) by A1115;
hence (v100 "/\" (v101 "/\" (v101 "\/" v1))) "\/" (v101 "/\" v103) = v101 "/\" (v103 "\/" (v100 "/\" (v101 "\/" (v101 "/\" v1)))) by A123; :: thesis:

end;

A1413: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v1 "/\" (v3 "\/" (v0 "/\" (v1 "\/" v2))) = v1 "/\" (v3 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2))))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" (v1 "\/" v2))) "\/" (v1 "/\" v3) = v1 "/\" (v3 "\/" (v0 "/\" (v1 "\/" v2))) by A123;
hence v1 "/\" (v3 "\/" (v0 "/\" (v1 "\/" v2))) = v1 "/\" (v3 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v2)))) by A1410; :: thesis:

end;

A1443: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" v2)) = v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v2)))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "/\" (v0 "\/" v2)) by A1165;
hence v0 "/\" (v1 "/\" (v0 "\/" v2)) = v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v2))) by A833; :: thesis:

end;

A1455: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "\/" (v1 "/\" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v1 "\/" (v1 "\/" (v0 "/\" v2)))) = v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) by A1214;
hence v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "\/" (v1 "/\" (v1 "\/" v2)) by A1121; :: thesis:

end;

A1457: for v1, v2, v0 being Element of (BA2TBAA B) holds v1 "\/" (v0 "/\" (v0 "\/" v2)) = v0 "\/" (v1 "/\" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v1 "\/" (v0 "/\" v2))) = v1 "\/" (v0 "/\" (v0 "\/" v2)) by A1177;
hence v1 "\/" (v0 "/\" (v0 "\/" v2)) = v0 "\/" (v1 "/\" (v1 "\/" v2)) by A1455; :: thesis:

end;

A1470: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) by A1272;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) by A714; :: thesis:

end;

A1472: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" v2))) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0)))

proof

let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2)))) = v0 "/\" ((v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" v2))) by A1413;
hence v0 "/\" ((v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" v2))) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0))) by A994; :: thesis:

end;

A1474: for v1, v3, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" v3)) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0)))

proof

let v1, v3, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v0 "\/" v2)) = (v0 "\/" v2) "/\" (v1 "\/" v3) by A523;
hence v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" v3)) = v0 "/\" ((v0 "\/" v2) "/\" (v1 "\/" (v3 "/\" v0))) by A1472; :: thesis:

end;

A1482: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1))))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v1 "/\" (v0 "\/" v1))) = v0 "/\" (v1 "/\" (v0 "\/" v1)) by A1443;
hence v0 "\/" (v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1))))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A816; :: thesis:

end;

A1484: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" (v0 "\/" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1)))) = v0 "/\" (v1 "\/" (v1 "/\" (v0 "\/" v1))) by A378;
hence v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" (v0 "\/" v1)))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A1482; :: thesis:

end;

A1486: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" (v0 "\/" v1)))) = v0 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1))) by A1096;
hence v0 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A1484; :: thesis:

end;

A1488: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "/\" (v0 "\/" v1))) = v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v1))) by A1406;
hence v0 "\/" (v0 "/\" (v0 "\/" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A1486; :: thesis:

end;

A1490: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" (v1 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "/\" v1)) = v0 "/\" (v0 "\/" v1) ;
hence v0 "\/" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" (v1 "\/" v1)) by A1488; :: thesis:

end;

A1499: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) by A1474;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) by A1470; :: thesis:

end;

A1501: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "\/" v1)) = v0 "/\" (v0 "\/" v1) ;
hence v0 "\/" (v0 "/\" (v0 "\/" v1)) = v0 "/\" (v0 "\/" v1) by A1490; :: thesis:

end;

A1504: for v102, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" (v100 "\/" v1)) "\/" ((v100 "/\" (v100 "\/" v1)) "/\" v102) = (v100 "/\" (v100 "\/" v1)) "/\" (v100 "\/" v102)

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "/\" (v100 "\/" v1)) = v100 "/\" (v100 "\/" v1) by A1126;
hence (v100 "/\" (v100 "\/" v1)) "\/" ((v100 "/\" (v100 "\/" v1)) "/\" v102) = (v100 "/\" (v100 "\/" v1)) "/\" (v100 "\/" v102) by A6; :: thesis:

end;

A1509: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v0 "\/" v1)) "\/" (v0 "/\" ((v0 "\/" v1) "/\" v2)) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" v2) = v2 "/\" (v0 "/\" (v0 "\/" v1)) by A14;
hence (v0 "/\" (v0 "\/" v1)) "\/" (v0 "/\" ((v0 "\/" v1) "/\" v2)) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A1504; :: thesis:

end;

A1513: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "\/" (v2 "/\" (v0 "\/" v1))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "\/" (v0 "/\" (v2 "/\" (v0 "\/" v1))) = v0 "/\" ((v0 "\/" v1) "\/" (v2 "/\" (v0 "\/" v1))) by A6;
hence v0 "/\" ((v0 "\/" v1) "\/" (v2 "/\" (v0 "\/" v1))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A1509; :: thesis:

end;

A1515: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v2 "/\" (v0 "\/" v1)) = v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1))) by A181;
hence v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A1513; :: thesis:

end;

A1517: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "/\" v2)) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2)

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "\/" (v2 "/\" (v0 "\/" v1)))) = v0 "\/" (v0 "/\" (v1 "/\" v2)) by A1027;
hence v0 "\/" (v0 "/\" (v1 "/\" v2)) = (v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) by A1515; :: thesis:

end;

A1519: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "/\" v2)) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "/\" (v0 "\/" v2) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) by A292;
hence v0 "\/" (v0 "/\" (v1 "/\" v2)) = v0 "/\" ((v0 "\/" v1) "/\" (v0 "\/" v2)) by A1517; :: thesis:

end;

A1521: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v1 "/\" v2)) = v0 "/\" (v0 "\/" (v1 "/\" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v2) = v0 "\/" (v1 "/\" v2) by A4;
hence v0 "\/" (v0 "/\" (v1 "/\" v2)) = v0 "/\" (v0 "\/" (v1 "/\" v2)) by A1519; :: thesis:

end;

A1580: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "/\" v1)) = v0 "/\" (v0 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "/\" v1)) = v0 "\/" (v0 "/\" (v0 "/\" v1)) by A1521;
hence v0 "\/" (v0 "/\" (v0 "/\" v1)) = v0 "/\" (v0 "\/" v1) by A1115; :: thesis:

end;

A1582: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v1 "/\" (v0 "/\" v2))) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v1 "\/" (v0 "/\" v2)) = v1 "\/" (v1 "/\" (v0 "/\" v2)) by A1521;
hence v0 "/\" (v1 "\/" (v1 "/\" (v0 "/\" v2))) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A730; :: thesis:

end;

A1584: for v0, v1, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v1))) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v1) = v1 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v1))) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A1582; :: thesis:

end;

A1588: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v1 "/\" v2)) = v0 "/\" (v1 "/\" (v1 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v2))) = v0 "/\" (v1 "\/" (v1 "/\" v2)) by A378;
hence v0 "/\" (v1 "\/" (v1 "/\" v2)) = v0 "/\" (v1 "/\" (v1 "\/" v2)) by A1584; :: thesis:

end;

A1622: for v102, v1, v100 being Element of (BA2TBAA B) holds v100 "\/" ((v100 "/\" (v100 "\/" v1)) "\/" v102) = v102 "\/" (v100 "/\" (v100 "\/" v1))

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v100 "/\" (v100 "\/" v1)) = v100 "/\" (v100 "\/" v1) by A1501;
hence v100 "\/" ((v100 "/\" (v100 "\/" v1)) "\/" v102) = v102 "\/" (v100 "/\" (v100 "\/" v1)) by A8; :: thesis:

end;

A1669: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v2 "\/" (v1 "/\" (v1 "\/" v2)))) = v0 "/\" (v1 "\/" (v0 "/\" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v2 "\/" (v1 "/\" (v1 "\/" v2))) = v2 "\/" (v1 "/\" (v1 "\/" v2)) by A1622;
hence v0 "/\" (v0 "/\" (v2 "\/" (v1 "/\" (v1 "\/" v2)))) = v0 "/\" (v1 "\/" (v0 "/\" v2)) by A1037; :: thesis:

end;

A1672: for v0, v1, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" (v2 "\/" v1)))) = v0 "/\" (v2 "\/" (v0 "/\" v1))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v1 "\/" (v2 "/\" (v2 "\/" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" (v2 "\/" v1)))) by A398;
hence v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" (v2 "\/" v1)))) = v0 "/\" (v2 "\/" (v0 "/\" v1)) by A1669; :: thesis:

end;

A1674: for v0, v1, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v2 "\/" (v2 "/\" v1)))) = v0 "/\" (v2 "\/" (v0 "/\" v1))

proof

let v0, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" (v2 "\/" v1)) = v0 "/\" (v2 "\/" (v2 "/\" v1)) by A1588;
hence v0 "/\" (v1 "\/" (v0 "/\" (v2 "\/" (v2 "/\" v1)))) = v0 "/\" (v2 "\/" (v0 "/\" v1)) by A1672; :: thesis:

end;

A1677: for v102, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" (v100 "\/" v1)) "/\" ((v100 "/\" (v1 "/\" v1)) "\/" v102) = (v100 "/\" (v1 "/\" v1)) "\/" (v100 "/\" v102)

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v100 "/\" (v1 "/\" v1)) = v100 "/\" (v100 "\/" v1) by A1521;
hence (v100 "/\" (v100 "\/" v1)) "/\" ((v100 "/\" (v1 "/\" v1)) "\/" v102) = (v100 "/\" (v1 "/\" v1)) "\/" (v100 "/\" v102) by A4; :: thesis:

end;

A1682: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "\/" v1)) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) by A292;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2) by A1677; :: thesis:

end;

A1684: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) by A1474;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2) by A1682; :: thesis:

end;

A1686: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) by A1499;
hence v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" v2) by A1684; :: thesis:

end;

A1689: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v2))) = v0 "/\" ((v2 "/\" v2) "\/" v1)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v2 "/\" v2)) "\/" (v0 "/\" v1) = v0 "/\" ((v2 "/\" v2) "\/" v1) by A6;
hence v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v2))) = v0 "/\" ((v2 "/\" v2) "\/" v1) by A1686; :: thesis:

end;

A1694: for v101, v103 being Element of (BA2TBAA B) holds (v103 "/\" v101) "/\" ((v103 "/\" v101) "\/" v103) = v103 "/\" (v101 "\/" ((v103 "/\" v101) "/\" v103))

proof

let v101, v103 be Element of (BA2TBAA B); :: thesis:
(v103 "/\" v101) "\/" ((v103 "/\" v101) "/\" (v103 "/\" v103)) = (v103 "/\" v101) "/\" ((v103 "/\" v101) "\/" v103) by A1521;
hence (v103 "/\" v101) "/\" ((v103 "/\" v101) "\/" v103) = v103 "/\" (v101 "\/" ((v103 "/\" v101) "/\" v103)) by A159; :: thesis:

end;

A1699: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" ((v0 "/\" v1) "/\" v0))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) by A292;
hence v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" ((v0 "/\" v1) "/\" v0)) by A1694; :: thesis:

end;

A1701: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" v1)) = v0 "/\" (v1 "\/" ((v0 "/\" v1) "/\" v0))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "/\" (v0 "\/" v1)) by A1165;
hence v0 "/\" (v1 "/\" (v0 "\/" v1)) = v0 "/\" (v1 "\/" ((v0 "/\" v1) "/\" v0)) by A1699; :: thesis:

end;

A1707: for v102, v103, v1, v101 being Element of (BA2TBAA B) holds (v101 "/\" (v1 "/\" v1)) "\/" ((v101 "/\" v102) "\/" (v103 "/\" (v101 "/\" (v101 "\/" v1)))) = (v101 "/\" (v1 "/\" v1)) "\/" (v101 "/\" (v103 "\/" v102))

proof

let v102, v103, v1, v101 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v101 "/\" (v1 "/\" v1)) = v101 "/\" (v101 "\/" v1) by A1521;
hence (v101 "/\" (v1 "/\" v1)) "\/" ((v101 "/\" v102) "\/" (v103 "/\" (v101 "/\" (v101 "\/" v1)))) = (v101 "/\" (v1 "/\" v1)) "\/" (v101 "/\" (v103 "\/" v102)) by A150; :: thesis:

end;

A1710: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" v1)) "\/" ((v0 "/\" v2) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1)))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v3 "/\" (v0 "/\" (v0 "\/" v1)) = v3 "/\" (v0 "\/" (v0 "/\" v1)) by A1588;
hence (v0 "/\" (v1 "/\" v1)) "\/" ((v0 "/\" v2) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1)))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2)) by A1707; :: thesis:

end;

A1712: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" ((v1 "/\" v1) "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v1)) "\/" ((v0 "/\" v2) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1)))) = (v0 "/\" ((v1 "/\" v1) "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) by A341;
hence (v0 "/\" ((v1 "/\" v1) "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "/\" (v1 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2)) by A1710; :: thesis:

end;

A1719: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v2 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" ((v2 "/\" v2) "\/" (v1 "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v2 "/\" v2)) "\/" (v0 "/\" (v1 "\/" v3)) = v0 "/\" ((v2 "/\" v2) "\/" (v1 "\/" v3)) by A6;
hence (v0 "/\" (v1 "\/" (v2 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" ((v2 "/\" v2) "\/" (v1 "\/" v3)) by A1712; :: thesis:

end;

A1721: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v2 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v3 "\/" ((v2 "/\" v2) "\/" v1))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v2 "/\" v2) "\/" (v1 "\/" v3) = v3 "\/" ((v2 "/\" v2) "\/" v1) by A8;
hence (v0 "/\" (v1 "\/" (v2 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v3 "\/" ((v2 "/\" v2) "\/" v1)) by A1719; :: thesis:

end;

A1725: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v2 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" ((v2 "/\" v2) "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" ((v2 "/\" v2) "\/" v3) = v3 "\/" (v1 "\/" (v2 "/\" v2)) by A8;
hence (v0 "/\" (v1 "\/" (v2 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" ((v2 "/\" v2) "\/" v3)) by A1721; :: thesis:

end;

A1729: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v1 "/\" v1))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v1 "/\" v1)) by A1689;
hence v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v2 "\/" (v1 "/\" v1)) by A1499; :: thesis:

end;

A1732: for v102, v1, v100 being Element of (BA2TBAA B) holds v100 "/\" (((v100 "/\" v1) "\/" v102) "/\" (v100 "/\" (v100 "\/" v1))) = v100 "/\" ((v100 "/\" v1) "\/" (v100 "/\" v102))

proof

let v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "\/" (v100 "/\" (v100 "/\" v1)) = v100 "/\" (v100 "\/" v1) by A1580;
hence v100 "/\" (((v100 "/\" v1) "\/" v102) "/\" (v100 "/\" (v100 "\/" v1))) = v100 "/\" ((v100 "/\" v1) "\/" (v100 "/\" v102)) by A82; :: thesis:

end;

A1738: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v2) "/\" ((v1 "\/" (v0 "/\" v2)) "/\" v0)) = v0 "/\" ((v0 "/\" v2) "\/" (v0 "/\" v1))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" (v0 "/\" v2)) "/\" (v0 "/\" (v0 "\/" v2)) = (v0 "\/" v2) "/\" ((v1 "\/" (v0 "/\" v2)) "/\" v0) by A14;
hence v0 "/\" ((v0 "\/" v2) "/\" ((v1 "\/" (v0 "/\" v2)) "/\" v0)) = v0 "/\" ((v0 "/\" v2) "\/" (v0 "/\" v1)) by A1732; :: thesis:

end;

A1743: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v2 "\/" (v0 "/\" v1)) "/\" (v0 "\/" v1))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v2 "\/" (v0 "/\" v1)) "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v0 "/\" (v2 "\/" (v0 "/\" v1))) by A14;
hence v0 "/\" (v0 "/\" ((v2 "\/" (v0 "/\" v1)) "/\" (v0 "\/" v1))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2)) by A1738; :: thesis:

end;

A1749: for v2, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v1))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" v1))) = v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v1)) by A1474;
hence v0 "/\" (v0 "/\" ((v0 "\/" v1) "/\" (v2 "\/" v1))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2)) by A1743; :: thesis:

end;

A1753: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence v0 "/\" (v0 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2)) by A1749; :: thesis:

end;

A1755: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" v2))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v1 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" v2))) by A398;
hence v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" v2))) = v0 "/\" ((v0 "/\" v1) "\/" (v0 "/\" v2)) by A1753; :: thesis:

end;

A1757: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" v2))) = v0 "/\" (v0 "/\" (v1 "\/" v2))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" v2) = v0 "/\" (v1 "\/" v2) by A6;
hence v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" v2))) = v0 "/\" (v0 "/\" (v1 "\/" v2)) by A1755; :: thesis:

end;

A1795: for v102, v103, v1, v101 being Element of (BA2TBAA B) holds (v101 "/\" (v101 "/\" v1)) "\/" ((v101 "/\" v102) "\/" (v103 "/\" (v101 "/\" (v101 "\/" v1)))) = (v101 "/\" (v101 "/\" v1)) "\/" (v101 "/\" (v103 "\/" v102))

proof

let v102, v103, v1, v101 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v101 "/\" (v101 "/\" v1)) = v101 "/\" (v101 "\/" v1) by A1580;
hence (v101 "/\" (v101 "/\" v1)) "\/" ((v101 "/\" v102) "\/" (v103 "/\" (v101 "/\" (v101 "\/" v1)))) = (v101 "/\" (v101 "/\" v1)) "\/" (v101 "/\" (v103 "\/" v102)) by A150; :: thesis:

end;

A1798: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v0 "/\" v1)) "\/" ((v0 "/\" v2) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1)))) = (v0 "/\" (v0 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v3 "/\" (v0 "/\" (v0 "\/" v1)) = v3 "/\" (v0 "\/" (v0 "/\" v1)) by A1588;
hence (v0 "/\" (v0 "/\" v1)) "\/" ((v0 "/\" v2) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1)))) = (v0 "/\" (v0 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2)) by A1795; :: thesis:

end;

A1800: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" ((v0 "/\" v1) "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "/\" (v0 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2))

proof

let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "/\" v1)) "\/" ((v0 "/\" v2) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1)))) = (v0 "/\" ((v0 "/\" v1) "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) by A341;
hence (v0 "/\" ((v0 "/\" v1) "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = (v0 "/\" (v0 "/\" v1)) "\/" (v0 "/\" (v3 "\/" v2)) by A1798; :: thesis:

end;

A1807: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v0 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" ((v0 "/\" v2) "\/" (v1 "\/" v3))

proof

let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v0 "/\" v2)) "\/" (v0 "/\" (v1 "\/" v3)) = v0 "/\" ((v0 "/\" v2) "\/" (v1 "\/" v3)) by A6;
hence (v0 "/\" (v1 "\/" (v0 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" ((v0 "/\" v2) "\/" (v1 "\/" v3)) by A1800; :: thesis:

end;

A1809: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v0 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v3 "\/" ((v0 "/\" v2) "\/" v1))

proof

let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v2) "\/" (v1 "\/" v3) = v3 "\/" ((v0 "/\" v2) "\/" v1) by A8;
hence (v0 "/\" (v1 "\/" (v0 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v3 "\/" ((v0 "/\" v2) "\/" v1)) by A1807; :: thesis:

end;

A1813: for v3, v1, v2, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v0 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" ((v0 "/\" v2) "\/" v3))

proof

let v3, v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v1 "\/" ((v0 "/\" v2) "\/" v3) = v3 "\/" (v1 "\/" (v0 "/\" v2)) by A8;
hence (v0 "/\" (v1 "\/" (v0 "/\" v2))) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" ((v0 "/\" v2) "\/" v3)) by A1809; :: thesis:

end;

A1817: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "\/" v1)) = v0 "/\" (v1 "/\" (v0 "\/" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" (v0 "/\" v1))) = v0 "/\" (v0 "/\" (v1 "\/" v1)) by A1757;
hence v0 "/\" (v0 "/\" (v1 "\/" v1)) = v0 "/\" (v1 "/\" (v0 "\/" v1)) by A1701; :: thesis:

end;

A2027: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" v1) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "/\" v1)) = v0 "/\" (v0 "\/" v1) by A1521;
hence v0 "/\" (v0 "\/" v1) = v0 "\/" (v1 "/\" v0) ; :: thesis:

end;

A2080: for v102, v100 being Element of (BA2TBAA B) holds v102 "/\" ((v100 "\/" v102) "\/" ((v100 "\/" v102) "/\" (v100 "\/" v102))) = v102 "\/" (v100 "/\" v102)

proof

let v102, v100 be Element of (BA2TBAA B); :: thesis:
v102 "/\" ((v100 "\/" v102) "\/" ((v100 "\/" v102) "/\" (v100 "\/" v102))) = (v100 "\/" v102) "/\" (v102 "\/" v102) ;
hence v102 "/\" ((v100 "\/" v102) "\/" ((v100 "\/" v102) "/\" (v100 "\/" v102))) = v102 "\/" (v100 "/\" v102) by A4; :: thesis:

end;

A2089: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v0 "\/" v1) "\/" (v0 "\/" (v1 "/\" v1))) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v1) = v0 "\/" (v1 "/\" v1) ;
hence v0 "/\" ((v0 "\/" v1) "\/" (v0 "\/" (v1 "/\" v1))) = v0 "\/" (v1 "/\" v0) by A2080; :: thesis:

end;

A2091: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" ((v1 "/\" v1) "\/" (v0 "\/" v1))) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "/\" v1) "\/" (v0 "\/" v1)) = (v0 "\/" v1) "\/" (v0 "\/" (v1 "/\" v1)) by A8;
hence v0 "/\" (v0 "\/" ((v1 "/\" v1) "\/" (v0 "\/" v1))) = v0 "\/" (v1 "/\" v0) by A2089; :: thesis:

end;

A2097: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "\/" (v0 "\/" ((v1 "/\" v1) "\/" v1))) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "/\" v1) "\/" v1) = v1 "\/" (v0 "\/" (v1 "/\" v1)) by A8;
hence v0 "/\" (v0 "\/" (v0 "\/" ((v1 "/\" v1) "\/" v1))) = v0 "\/" (v1 "/\" v0) by A2091; :: thesis:

end;

A2101: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v1)))) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v0 "\/" (v1 "\/" (v1 "/\" v1)))) = v0 "\/" (v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v1)))) by A2027;
hence v0 "\/" (v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v1)))) = v0 "\/" (v1 "/\" v0) by A2097; :: thesis:

end;

A2103: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1)))) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "\/" (v1 "/\" v1))) = v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1))) by A2027;
hence v0 "\/" (v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1)))) = v0 "\/" (v1 "/\" v0) by A2101; :: thesis:

end;

A2105: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "\/" (v1 "/\" v1))) = v0 "\/" (v0 "/\" (v1 "/\" v1)) ;
hence v0 "\/" (v0 "\/" (v0 "/\" (v1 "/\" v1))) = v0 "\/" (v1 "/\" v0) by A2103; :: thesis:

end;

A2107: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "/\" (v0 "\/" v1)) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "/\" v1)) = v0 "/\" (v0 "\/" v1) by A1521;
hence v0 "\/" (v0 "/\" (v0 "\/" v1)) = v0 "\/" (v1 "/\" v0) by A2105; :: thesis:

end;

A2109: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v0 "\/" (v0 "/\" v1)) = v0 "\/" (v1 "/\" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" v1) by A2027;
hence v0 "\/" (v0 "\/" (v0 "/\" v1)) = v0 "\/" (v1 "/\" v0) by A2107; :: thesis:

end;

A2117: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "\/" (v0 "/\" (v1 "/\" v0)) = v0 "/\" (v1 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "/\" v0) = v0 "/\" (v1 "/\" v0) by A14;
hence (v0 "/\" v1) "\/" (v0 "/\" (v1 "/\" v0)) = v0 "/\" (v1 "\/" v1) ; :: thesis:

end;

A2121: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" (v0 "/\" v1)) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A6;
hence v0 "/\" (v1 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v1) by A2117; :: thesis:

end;

A2148: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v0 "/\" (v1 "\/" v1)) = v1 "/\" (v0 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "\/" (v0 "/\" v0)) = v1 "/\" (v0 "\/" v0) ;
hence v0 "/\" (v0 "/\" (v1 "\/" v1)) = v1 "/\" (v0 "\/" v0) by A292; :: thesis:

end;

A2170: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "/\" (v0 "\/" v0))) "/\" (v2 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" ((v1 "/\" v1) "\/" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "\/" ((v1 "/\" v1) "\/" v2) = v2 "\/" (v1 "\/" (v1 "/\" v1)) by A8;
hence (v0 "\/" (v1 "/\" (v0 "\/" v0))) "/\" (v2 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" ((v1 "/\" v1) "\/" v2)) by A85; :: thesis:

end;

A2178: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" (v0 "\/" v1)) = v1 "/\" (v0 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" ((v1 "/\" v1) "\/" (v0 "/\" v1)) = (v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" (v0 "\/" v1)) by A336;
hence (v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" (v0 "\/" v1)) = v1 "/\" (v0 "\/" v0) by A85; :: thesis:

end;

A2180: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" v1) = v1 "/\" (v0 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v1 "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" v1) by A14;
hence (v0 "\/" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "/\" v1) = v1 "/\" (v0 "\/" v0) by A2178; :: thesis:

end;

A2184: for v1, v0 being Element of (BA2TBAA B) holds v1 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "\/" v1)) = v1 "/\" (v0 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) by A14;
hence v1 "/\" ((v0 "\/" (v0 "/\" v1)) "/\" (v0 "\/" v1)) = v1 "/\" (v0 "\/" v0) by A2180; :: thesis:

end;

A2189: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v0))) = v0 "/\" (v1 "\/" v1)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v0) "/\" (v1 "\/" (v1 "/\" v0)) = v1 "\/" (v0 "/\" (v1 "/\" v0)) by A4;
hence v0 "/\" (v1 "\/" (v0 "/\" (v1 "/\" v0))) = v0 "/\" (v1 "\/" v1) by A2184; :: thesis:

end;

A2191: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v1 "/\" (v0 "/\" v0))) = v0 "/\" (v1 "\/" v1)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "/\" v0) = v0 "/\" (v1 "/\" v0) by A14;
hence v0 "/\" (v1 "\/" (v1 "/\" (v0 "/\" v0))) = v0 "/\" (v1 "\/" v1) by A2189; :: thesis:

end;

A2193: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v1 "\/" v0)) = v0 "/\" (v1 "\/" v1)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v1 "/\" (v0 "/\" v0)) = v1 "/\" (v1 "\/" v0) by A1521;
hence v0 "/\" (v1 "/\" (v1 "\/" v0)) = v0 "/\" (v1 "\/" v1) by A2191; :: thesis:

end;

A2195: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v1 "/\" v0)) = v0 "/\" (v1 "\/" v1)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v1 "\/" v0) = v1 "\/" (v1 "/\" v0) by A2027;
hence v0 "/\" (v1 "\/" (v1 "/\" v0)) = v0 "/\" (v1 "\/" v1) by A2193; :: thesis:

end;

A2212: for v101, v100 being Element of (BA2TBAA B) holds (v100 "/\" v101) "/\" ((v100 "\/" (v100 "/\" v101)) "\/" ((v100 "\/" (v100 "/\" v101)) "/\" (v100 "\/" (v100 "/\" v101)))) = v100 "/\" (v101 "\/" (v100 "/\" v101))

proof

let v101, v100 be Element of (BA2TBAA B); :: thesis:
(v100 "/\" v101) "/\" ((v100 "\/" (v100 "/\" v101)) "\/" ((v100 "\/" (v100 "/\" v101)) "/\" (v100 "\/" (v100 "/\" v101)))) = (v100 "\/" (v100 "/\" v101)) "/\" ((v100 "/\" v101) "\/" (v100 "/\" v101)) ;
hence (v100 "/\" v101) "/\" ((v100 "\/" (v100 "/\" v101)) "\/" ((v100 "\/" (v100 "/\" v101)) "/\" (v100 "\/" (v100 "/\" v101)))) = v100 "/\" (v101 "\/" (v100 "/\" v101)) by A85; :: thesis:

end;

A2215: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" ((v0 "/\" v1) "/\" (v0 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v0 "\/" (v0 "/\" v1)) = v0 "\/" ((v0 "/\" v1) "/\" (v0 "/\" v1)) ;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" ((v0 "/\" v1) "/\" (v0 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2212; :: thesis:

end;

A2217: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v1 "/\" ((v0 "/\" v1) "/\" v0)))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "/\" (v0 "/\" v1) = v1 "/\" ((v0 "/\" v1) "/\" v0) by A14;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v1 "/\" ((v0 "/\" v1) "/\" v0)))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2215; :: thesis:

end;

A2221: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" ((v0 "/\" v1) "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" ((v0 "/\" v1) "/\" v1) = v1 "/\" (v0 "/\" (v0 "/\" v1)) by A14;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" ((v0 "/\" v1) "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2217; :: thesis:

end;

A2225: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "/\" v1) = v1 "/\" (v0 "/\" v1) by A14;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" v1))))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2221; :: thesis:

end;

A2227: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "\/" (v1 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v0 "/\" (v1 "/\" v1))) = v0 "/\" (v0 "\/" (v1 "/\" v1)) by A1580;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "\/" (v1 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2225; :: thesis:

end;

A2229: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" (v1 "/\" v1)) = v0 "\/" (v0 "/\" (v1 "/\" v1)) by A2027;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" (v1 "/\" v1)))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2227; :: thesis:

end;

A2231: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "\/" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "/\" v1)) = v0 "/\" (v0 "\/" v1) by A1521;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "/\" (v0 "\/" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2229; :: thesis:

end;

A2233: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" v1) by A2027;
hence (v0 "/\" v1) "/\" ((v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2231; :: thesis:

end;

A2235: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "/\" v1) "\/" ((v0 "\/" (v0 "/\" v1)) "\/" v0)) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "\/" (v0 "\/" (v0 "/\" v1)) = (v0 "/\" v1) "\/" ((v0 "\/" (v0 "/\" v1)) "\/" v0) by A8;
hence (v0 "/\" v1) "/\" ((v0 "/\" v1) "\/" ((v0 "\/" (v0 "/\" v1)) "\/" v0)) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2233; :: thesis:

end;

A2239: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" ((v0 "/\" v1) "\/" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "\/" (v0 "/\" v1)) = v0 "\/" (v0 "/\" v1) by A2109;
hence (v0 "/\" v1) "/\" ((v0 "/\" v1) "\/" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2235; :: thesis:

end;

A2241: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" (v0 "\/" ((v0 "/\" v1) "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v1) "\/" (v0 "/\" v1)) = (v0 "/\" v1) "\/" (v0 "\/" (v0 "/\" v1)) by A8;
hence (v0 "/\" v1) "/\" (v0 "\/" ((v0 "/\" v1) "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2239; :: thesis:

end;

A2243: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" (v0 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v0 "/\" v1) = v0 "/\" (v1 "\/" v1) ;
hence (v0 "/\" v1) "/\" (v0 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2241; :: thesis:

end;

A2245: for v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v0 "/\" (v1 "\/" v1)) = v0 "\/" (v0 "/\" v1) ;
hence (v0 "/\" v1) "/\" (v0 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2243; :: thesis:

end;

A2247: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

end;

A2249: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" v0)) = v0 "/\" (v1 "\/" (v0 "/\" v1))

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "\/" (v0 "/\" v1)) = v1 "/\" (v0 "\/" v0) by A2195;
hence v0 "/\" (v1 "/\" (v0 "\/" v0)) = v0 "/\" (v1 "\/" (v0 "/\" v1)) by A2247; :: thesis:

end;

A2251: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" v0)) = v0 "/\" (v1 "\/" v1)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v1) by A2121;
hence v0 "/\" (v1 "/\" (v0 "\/" v0)) = v0 "/\" (v1 "\/" v1) by A2249; :: thesis:

end;

A2340: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v0 "\/" v1)) = v0 "\/" ((v0 "/\" v0) "\/" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v0) "\/" v1) = v1 "\/" (v0 "\/" (v0 "/\" v0)) by A8;
hence v0 "\/" (v1 "/\" (v0 "\/" v1)) = v0 "\/" ((v0 "/\" v0) "\/" v1) by A1457; :: thesis:

end;

A2355: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" ((v0 "/\" v0) "\/" v2)) = v0 "\/" (v1 "/\" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v0) "\/" v2) = v2 "\/" (v0 "\/" (v0 "/\" v0)) by A8;
hence (v0 "\/" v1) "/\" (v0 "\/" ((v0 "/\" v0) "\/" v2)) = v0 "\/" (v1 "/\" v2) by A4; :: thesis:

end;

A2359: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" (v0 "\/" v2)) = v0 "\/" (v1 "/\" v2)

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v2 "\/" (v0 "/\" v0))) = (v0 "\/" v1) "/\" (v0 "\/" (v0 "\/" v2)) ;
hence (v0 "\/" v1) "/\" (v0 "\/" (v0 "\/" v2)) = v0 "\/" (v1 "/\" v2) by A2355; :: thesis:

end;

A2361: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v0 "\/" v2)) = v0 "\/" (v1 "/\" v2)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v0 "\/" v2)) = v0 "\/" (v1 "/\" (v0 "\/" v2)) by A4;
hence v0 "\/" (v1 "/\" (v0 "\/" v2)) = v0 "\/" (v1 "/\" v2) by A2359; :: thesis:

end;

A2369: for v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" v1)) = v1 "/\" (v0 "\/" v0)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "/\" (v1 "\/" v1)) = v1 "/\" (v0 "\/" v0) by A2148;
hence v0 "/\" (v1 "/\" (v0 "\/" v1)) = v1 "/\" (v0 "\/" v0) by A1817; :: thesis:

end;

A2371: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "/\" v0)) "/\" (v2 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v1)))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v0 "\/" v0)) = v0 "\/" (v1 "/\" v0) ;
hence (v0 "\/" (v1 "/\" v0)) "/\" (v2 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v1))) by A2170; :: thesis:

end;

A2375: for v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" (v1 "\/" v2))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v1 "\/" (v1 "\/" v2)) ;
hence (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v0 "/\" (v1 "\/" v1))) = v0 "/\" (v1 "\/" (v1 "\/" v2)) by A2371; :: thesis:

end;

A2397: for v0, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "\/" (v0 "/\" v0)) = v0 "\/" (v1 "/\" v1)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "/\" (v0 "\/" v1)) = v0 "\/" (v1 "/\" v1) by A2361;
hence v0 "\/" (v1 "\/" (v0 "/\" v0)) = v0 "\/" (v1 "/\" v1) by A2340; :: thesis:

end;

A2408: c2 "\/" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))) = c2 "\/" ((c3 "\/" c4) "/\" (c3 "/\" c4)) by A2361;
A2411: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3))))) = (c2 "\/" (c4 "/\" ((c3 "\/" c4) "/\" c3))) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A14, A2408, A368;
A2415: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3))))) = (c2 "\/" (c4 "/\" (c3 "\/" (c3 "/\" c4)))) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A2027, A2411;
A2417: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3))))) = (c2 "\/" (c4 "/\" (c3 "\/" c3))) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A2195, A2415;
A2431: for v2, v0, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v1 "/\" v0)) = v0 "/\" (v1 "\/" (v1 "\/" v2))

proof

let v2, v0, v1 be Element of (BA2TBAA B); :: thesis:
v2 "\/" (v0 "/\" (v1 "\/" v1)) = v2 "\/" (v1 "/\" v0) ;
hence (v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v1 "/\" v0)) = v0 "/\" (v1 "\/" (v1 "\/" v2)) by A2375; :: thesis:

end;

A2435: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" v2) = v0 "/\" (v1 "\/" (v1 "\/" v2))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v0 "/\" v1)) "/\" (v2 "\/" (v0 "/\" v1)) = v0 "/\" (v1 "\/" v2) by A85;
hence v0 "/\" (v1 "\/" v2) = v0 "/\" (v1 "\/" (v1 "\/" v2)) by A2431; :: thesis:

end;

A2490: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" v2)) = v0 "/\" (v2 "\/" (v1 "/\" v1))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence v0 "/\" (v1 "\/" (v0 "/\" v2)) = v0 "/\" (v2 "\/" (v1 "/\" v1)) by A1729; :: thesis:

end;

A2492: for v1, v2, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v0 "/\" v2)) = v0 "/\" (v2 "\/" v1)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "\/" (v1 "/\" v1)) = v0 "/\" (v2 "\/" v1) ;
hence v0 "/\" (v1 "\/" (v0 "/\" v2)) = v0 "/\" (v2 "\/" v1) by A2490; :: thesis:

end;

A2498: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v2))) = v0 "/\" (v2 "\/" (v0 "/\" v1))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" (v2 "\/" (v1 "/\" v2)))) = v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v2))) by A2492;
hence v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v2))) = v0 "/\" (v2 "\/" (v0 "/\" v1)) by A1674; :: thesis:

end;

A2500: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v2))) = v0 "/\" (v2 "\/" v1)

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "\/" (v0 "/\" v1)) = v0 "/\" (v2 "\/" v1) by A2492;
hence v0 "/\" (v1 "\/" (v2 "\/" (v1 "/\" v2))) = v0 "/\" (v2 "\/" v1) by A2498; :: thesis:

end;

A2504: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" (v3 "\/" (v0 "/\" v2)))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v0 "/\" v2)) = v0 "/\" (v1 "\/" v2) by A2492;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" (v3 "\/" (v0 "/\" v2))) by A1813; :: thesis:

end;

A2506: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v3 "\/" (v2 "/\" v2))) = v0 "/\" (v1 "\/" (v3 "\/" (v0 "/\" v2)))

proof

let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v2))) = v0 "/\" (v1 "\/" (v3 "\/" (v2 "/\" v2))) by A1725;
hence v0 "/\" (v1 "\/" (v3 "\/" (v2 "/\" v2))) = v0 "/\" (v1 "\/" (v3 "\/" (v0 "/\" v2))) by A2504; :: thesis:

end;

A2509: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" (v1 "/\" v2))) "\/" (v1 "/\" (v2 "\/" v3)) = v1 "/\" (v0 "\/" (v3 "\/" (v2 "/\" v2)))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" (v0 "\/" v2)) "\/" (v3 "/\" (v1 "\/" (v1 "/\" v2))) = v1 "/\" (v0 "\/" (v3 "\/" (v2 "/\" v2))) by A1725;
hence (v0 "/\" (v1 "\/" (v1 "/\" v2))) "\/" (v1 "/\" (v2 "\/" v3)) = v1 "/\" (v0 "\/" (v3 "\/" (v2 "/\" v2))) by A444; :: thesis:

end;

A2512: for v102, v100 being Element of (BA2TBAA B) holds Tern (v100,(v100 "\/" v102),v102) = (v100 "\/" v102) "\/" ((v100 "\/" v102) "/\" (v100 "/\" v102))

proof

let v102, v100 be Element of (BA2TBAA B); :: thesis:
(v100 "\/" v102) "/\" ((v100 "\/" v102) "\/" (v100 "/\" v102)) = (v100 "\/" v102) "\/" ((v100 "\/" v102) "/\" (v100 "/\" v102)) by A2027;
hence Tern (v100,(v100 "\/" v102),v102) = (v100 "\/" v102) "\/" ((v100 "\/" v102) "/\" (v100 "/\" v102)) by A63; :: thesis:

end;

A2515: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v0 "/\" v1)) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
Tern (v0,(v0 "\/" v1),v1) = (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v0 "/\" v1)) by A63;
hence (v0 "\/" v1) "/\" ((v0 "\/" v1) "\/" (v0 "/\" v1)) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1)) by A2512; :: thesis:

end;

A2517: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v0 "/\" v1) = v0 "\/" (v1 "\/" (v0 "/\" v1)) by A181;
hence (v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1)) by A2515; :: thesis:

end;

A2519: for v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" v1) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v1 "\/" (v0 "/\" v1))) = (v0 "\/" v1) "/\" (v0 "\/" v1) by A2500;
hence (v0 "\/" v1) "/\" (v0 "\/" v1) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1)) by A2517; :: thesis:

end;

A2521: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" v1) = v0 "\/" (v1 "/\" v1) ;
hence v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" ((v0 "\/" v1) "/\" (v0 "/\" v1)) by A2519; :: thesis:

end;

A2523: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v1 "/\" ((v0 "\/" v1) "/\" v0))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "/\" v1) = v1 "/\" ((v0 "\/" v1) "/\" v0) by A14;
hence v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v1 "/\" ((v0 "\/" v1) "/\" v0)) by A2521; :: thesis:

end;

A2527: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1)))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" v1) by A2027;
hence v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v1 "/\" (v0 "\/" (v0 "/\" v1))) by A2523; :: thesis:

end;

A2529: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v1 "/\" (v0 "\/" v0))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "\/" (v0 "/\" v1)) = v1 "/\" (v0 "\/" v0) by A2195;
hence v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v1 "/\" (v0 "\/" v0)) by A2527; :: thesis:

end;

A2531: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v0 "/\" v1)

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v1 "/\" (v0 "\/" v0)) = (v0 "\/" v1) "\/" (v0 "/\" v1) ;
hence v0 "\/" (v1 "/\" v1) = (v0 "\/" v1) "\/" (v0 "/\" v1) by A2529; :: thesis:

end;

A2533: for v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v1) = v0 "\/" (v1 "\/" (v0 "/\" v1))

proof

let v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "\/" (v0 "/\" v1) = v0 "\/" (v1 "\/" (v0 "/\" v1)) by A181;
hence v0 "\/" (v1 "/\" v1) = v0 "\/" (v1 "\/" (v0 "/\" v1)) by A2531; :: thesis:

end;

A2549: for v103, v100, v1, v101 being Element of (BA2TBAA B) holds (v100 "/\" (v101 "\/" (v101 "/\" v1))) "\/" (v101 "/\" v103) = v101 "/\" (v103 "\/" (v100 "/\" (v101 "\/" v1)))

proof

let v103, v100, v1, v101 be Element of (BA2TBAA B); :: thesis:
v101 "/\" (v101 "\/" v1) = v101 "\/" (v101 "/\" v1) by A2027;
hence (v100 "/\" (v101 "\/" (v101 "/\" v1))) "\/" (v101 "/\" v103) = v101 "/\" (v103 "\/" (v100 "/\" (v101 "\/" v1))) by A123; :: thesis:

end;

A2553: for v101, v102, v1, v100 being Element of (BA2TBAA B) holds (v100 "/\" v101) "\/" (v102 "/\" (v100 "\/" (v100 "/\" v1))) = v100 "/\" (v101 "\/" (v102 "/\" (v100 "\/" v1)))

proof

let v101, v102, v1, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v100 "\/" v1) = v100 "\/" (v100 "/\" v1) by A2027;
hence (v100 "/\" v101) "\/" (v102 "/\" (v100 "\/" (v100 "/\" v1))) = v100 "/\" (v101 "\/" (v102 "/\" (v100 "\/" v1))) by A159; :: thesis:

end;

A2556: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds v1 "/\" ((v2 "\/" v3) "\/" (v0 "/\" (v1 "\/" v2))) = v1 "/\" (v0 "\/" (v3 "\/" (v2 "/\" v2)))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "\/" (v1 "/\" v2))) "\/" (v1 "/\" (v2 "\/" v3)) = v1 "/\" ((v2 "\/" v3) "\/" (v0 "/\" (v1 "\/" v2))) by A2549;
hence v1 "/\" ((v2 "\/" v3) "\/" (v0 "/\" (v1 "\/" v2))) = v1 "/\" (v0 "\/" (v3 "\/" (v2 "/\" v2))) by A2509; :: thesis:

end;

A2559: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" (v0 "\/" v1)))) = v0 "/\" (v3 "\/" (v2 "\/" (v1 "/\" v1)))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v2) "\/" (v3 "/\" (v0 "\/" v1)) = v1 "\/" (v2 "\/" (v3 "/\" (v0 "\/" v1))) by A181;
hence v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" (v0 "\/" v1)))) = v0 "/\" (v3 "\/" (v2 "\/" (v1 "/\" v1))) by A2556; :: thesis:

end;

A2561: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" ((v1 "\/" v2) "\/" (v3 "/\" (v0 "\/" v1))) = v0 "/\" (v1 "\/" (v2 "\/" v3))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v0 "\/" (v0 "/\" v1))) = v0 "/\" ((v1 "\/" v2) "\/" (v3 "/\" (v0 "\/" v1))) by A2553;
hence v0 "/\" ((v1 "\/" v2) "\/" (v3 "/\" (v0 "\/" v1))) = v0 "/\" (v1 "\/" (v2 "\/" v3)) by A458; :: thesis:

end;

A2563: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" (v0 "\/" v1)))) = v0 "/\" (v1 "\/" (v2 "\/" v3))

proof

end;

A2565: for v0, v3, v1, v2 being Element of (BA2TBAA B) holds v0 "/\" (v3 "\/" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v1 "\/" (v2 "\/" v3))

proof

let v0, v3, v1, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" (v0 "\/" v1)))) = v0 "/\" (v3 "\/" (v2 "\/" (v1 "/\" v1))) by A2559;
hence v0 "/\" (v3 "\/" (v2 "\/" (v1 "/\" v1))) = v0 "/\" (v1 "\/" (v2 "\/" v3)) by A2563; :: thesis:

end;

A2574: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v3 "\/" (v1 "\/" v2)) = v0 "/\" (v1 "\/" (v2 "\/" (v0 "/\" v3)))

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" v3))) = v0 "/\" (v3 "\/" (v1 "\/" v2)) by A2565;
hence v0 "/\" (v3 "\/" (v1 "\/" v2)) = v0 "/\" (v1 "\/" (v2 "\/" (v0 "/\" v3))) by A2506; :: thesis:

end;

A2577: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v3 "\/" (v1 "\/" v2)) = v0 "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1)))

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v2 "\/" v3) = v3 "\/" (v1 "\/" v2) by A8;
hence v0 "/\" (v3 "\/" (v1 "\/" v2)) = v0 "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1))) by A2574; :: thesis:

end;

A2583: for v0, v2, v1, v3 being Element of (BA2TBAA B) holds v0 "/\" (v2 "\/" (v3 "\/" v1)) = v0 "/\" (v2 "\/" (v1 "\/" (v0 "/\" v3)))

proof

let v0, v2, v1, v3 be Element of (BA2TBAA B); :: thesis:
v2 "\/" (v3 "\/" v1) = v1 "\/" (v2 "\/" v3) by A8;
hence v0 "/\" (v2 "\/" (v3 "\/" v1)) = v0 "/\" (v2 "\/" (v1 "\/" (v0 "/\" v3))) by A2577; :: thesis:

end;

A2591: for v102, v103, v1, v101 being Element of (BA2TBAA B) holds (v101 "\/" v1) "/\" ((v101 "\/" v102) "/\" (v103 "\/" (v101 "/\" (v101 "\/" v1)))) = v101 "\/" (v1 "/\" (v103 "/\" v102))

proof

let v102, v103, v1, v101 be Element of (BA2TBAA B); :: thesis:
(v101 "\/" v1) "/\" (v101 "\/" (v103 "/\" v102)) = v101 "\/" (v1 "/\" (v103 "/\" v102)) by A4;
hence (v101 "\/" v1) "/\" ((v101 "\/" v102) "/\" (v103 "\/" (v101 "/\" (v101 "\/" v1)))) = v101 "\/" (v1 "/\" (v103 "/\" v102)) by A241; :: thesis:

end;

A2594: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v2) "/\" (v3 "\/" (v0 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v3 "/\" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v0 "\/" v1) = v0 "\/" (v0 "/\" v1) by A2027;
hence (v0 "\/" v1) "/\" ((v0 "\/" v2) "/\" (v3 "\/" (v0 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v3 "/\" v2)) by A2591; :: thesis:

end;

A2596: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" ((v0 "\/" v2) "/\" (v0 "\/" ((v0 "/\" v1) "\/" v3))) = v0 "\/" (v1 "/\" (v3 "/\" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v0 "/\" v1) "\/" v3) = v3 "\/" (v0 "\/" (v0 "/\" v1)) by A8;
hence (v0 "\/" v1) "/\" ((v0 "\/" v2) "/\" (v0 "\/" ((v0 "/\" v1) "\/" v3))) = v0 "\/" (v1 "/\" (v3 "/\" v2)) by A2594; :: thesis:

end;

A2600: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds (v0 "\/" v1) "/\" (v0 "\/" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v3 "/\" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v2) "/\" (v0 "\/" (v3 "\/" (v0 "/\" v1))) = v0 "\/" (v2 "/\" (v3 "\/" (v0 "/\" v1))) by A4;
hence (v0 "\/" v1) "/\" (v0 "\/" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v3 "/\" v2)) by A2596; :: thesis:

end;

A2602: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v3 "/\" v2))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v0 "\/" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) by A4;
hence v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = v0 "\/" (v1 "/\" (v3 "/\" v2)) by A2600; :: thesis:

end;

A2618: for v0, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "/\" (v0 "\/" v0)) = v1 "/\" (v0 "\/" v0)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v1 "\/" v1) = v0 "/\" (v1 "/\" (v0 "\/" v0)) by A2251;
hence v0 "/\" (v1 "/\" (v0 "\/" v0)) = v1 "/\" (v0 "\/" v0) ; :: thesis:

end;

A2652: for v1, v2, v100, v102, v101 being Element of (BA2TBAA B) holds (v100 "\/" (v101 "\/" v102)) "/\" (v101 "\/" (v1 "/\" v2)) = v101 "\/" ((v1 "/\" (v101 "\/" v2)) "/\" (v100 "\/" v102))

proof

let v1, v2, v100, v102, v101 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v1 "/\" (v101 "\/" v2)) = v101 "\/" (v1 "/\" v2) by A2361;
hence (v100 "\/" (v101 "\/" v102)) "/\" (v101 "\/" (v1 "/\" v2)) = v101 "\/" ((v1 "/\" (v101 "\/" v2)) "/\" (v100 "\/" v102)) by A109; :: thesis:

end;

A2655: for v1, v0, v2, v4, v3 being Element of (BA2TBAA B) holds v1 "\/" ((v3 "/\" v4) "/\" (v0 "\/" v2)) = v1 "\/" ((v3 "/\" (v1 "\/" v4)) "/\" (v0 "\/" v2))

proof

let v1, v0, v2, v4, v3 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" v2)) "/\" (v1 "\/" (v3 "/\" v4)) = v1 "\/" ((v3 "/\" v4) "/\" (v0 "\/" v2)) by A109;
hence v1 "\/" ((v3 "/\" v4) "/\" (v0 "\/" v2)) = v1 "\/" ((v3 "/\" (v1 "\/" v4)) "/\" (v0 "\/" v2)) by A2652; :: thesis:

end;

A2658: for v0, v1, v2, v4, v3 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" v4))) = v0 "\/" ((v1 "/\" (v0 "\/" v2)) "/\" (v3 "\/" v4))

proof

let v0, v1, v2, v4, v3 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v2) "/\" (v3 "\/" v4) = v1 "/\" (v2 "/\" (v3 "\/" v4)) by A292;
hence v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" v4))) = v0 "\/" ((v1 "/\" (v0 "\/" v2)) "/\" (v3 "\/" v4)) by A2655; :: thesis:

end;

A2660: for v0, v1, v2, v4, v3 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" v4))) = v0 "\/" (v1 "/\" ((v0 "\/" v2) "/\" (v3 "\/" v4)))

proof

let v0, v1, v2, v4, v3 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" (v0 "\/" v2)) "/\" (v3 "\/" v4) = v1 "/\" ((v0 "\/" v2) "/\" (v3 "\/" v4)) by A292;
hence v0 "\/" (v1 "/\" (v2 "/\" (v3 "\/" v4))) = v0 "\/" (v1 "/\" ((v0 "\/" v2) "/\" (v3 "\/" v4))) by A2658; :: thesis:

end;

A2663: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c4 "/\" (c3 "/\" (c1 "\/" (c2 "/\" c3))))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A2660, A2417;
A2667: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c3 "/\" (c4 "/\" (c1 "\/" (c2 "/\" c3))))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A2663, A14;
A2669: not (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) "/\" (c2 "\/" (c3 "/\" (c4 "/\" c1))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A2602, A2667;
A2677: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "\/" c3) "/\" (c1 "\/" (c2 "/\" c3)))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A14, A2669;
A2680: for v103, v101, v100 being Element of (BA2TBAA B) holds (v101 "/\" (v100 "\/" v100)) "\/" ((v100 "\/" v101) "/\" v103) = (v100 "\/" v101) "/\" (v103 "\/" (v100 "/\" v101))

proof

let v103, v101, v100 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v101 "/\" (v100 "\/" v101)) = v101 "/\" (v100 "\/" v100) by A2369;
hence (v101 "/\" (v100 "\/" v100)) "\/" ((v100 "\/" v101) "/\" v103) = (v100 "\/" v101) "/\" (v103 "\/" (v100 "/\" v101)) by A131; :: thesis:

end;

A2692: for v103, v100, v1, v101 being Element of (BA2TBAA B) holds (v100 "\/" (v101 "\/" (v1 "/\" v1))) "/\" ((v1 "\/" (v101 "/\" v101)) "\/" v103) = (v1 "\/" (v101 "/\" v101)) "\/" (v103 "/\" (v100 "\/" v101))

proof

let v103, v100, v1, v101 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v1 "\/" (v101 "/\" v101)) = v101 "\/" (v1 "/\" v1) by A2397;
hence (v100 "\/" (v101 "\/" (v1 "/\" v1))) "/\" ((v1 "\/" (v101 "/\" v101)) "\/" v103) = (v1 "\/" (v101 "/\" v101)) "\/" (v103 "/\" (v100 "\/" v101)) by A117; :: thesis:

end;

A2697: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v2 "\/" ((v1 "/\" v1) "\/" v3)) = (v2 "\/" (v1 "/\" v1)) "\/" (v3 "/\" (v0 "\/" v1))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "\/" ((v1 "/\" v1) "\/" v3) = v3 "\/" (v2 "\/" (v1 "/\" v1)) by A8;
hence (v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v2 "\/" ((v1 "/\" v1) "\/" v3)) = (v2 "\/" (v1 "/\" v1)) "\/" (v3 "/\" (v0 "\/" v1)) by A2692; :: thesis:

end;

A2701: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v1 "\/" (v2 "\/" v3)) = (v2 "\/" (v1 "/\" v1)) "\/" (v3 "/\" (v0 "\/" v1))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v2 "\/" (v3 "\/" (v1 "/\" v1))) = (v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v1 "\/" (v2 "\/" v3)) by A2565;
hence (v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v1 "\/" (v2 "\/" v3)) = (v2 "\/" (v1 "/\" v1)) "\/" (v3 "/\" (v0 "\/" v1)) by A2697; :: thesis:

end;

A2703: for v1, v0, v3, v2 being Element of (BA2TBAA B) holds v1 "\/" ((v2 "\/" v3) "/\" (v0 "\/" (v2 "/\" v2))) = (v2 "\/" (v1 "/\" v1)) "\/" (v3 "/\" (v0 "\/" v1))

proof

let v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v1 "\/" (v2 "\/" v3)) = v1 "\/" ((v2 "\/" v3) "/\" (v0 "\/" (v2 "/\" v2))) by A109;
hence v1 "\/" ((v2 "\/" v3) "/\" (v0 "\/" (v2 "/\" v2))) = (v2 "\/" (v1 "/\" v1)) "\/" (v3 "/\" (v0 "\/" v1)) by A2701; :: thesis:

end;

A2706: for v0, v3, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" ((v1 "\/" v2) "/\" (v3 "\/" v1)) = (v1 "\/" (v0 "/\" v0)) "\/" (v2 "/\" (v3 "\/" v0))

proof

let v0, v3, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v2) "/\" (v3 "\/" (v1 "/\" v1)) = (v1 "\/" v2) "/\" (v3 "\/" v1) ;
hence v0 "\/" ((v1 "\/" v2) "/\" (v3 "\/" v1)) = (v1 "\/" (v0 "/\" v0)) "\/" (v2 "/\" (v3 "\/" v0)) by A2703; :: thesis:

end;

A2708: for v0, v1, v2, v3 being Element of (BA2TBAA B) holds v0 "\/" (v1 "\/" (v3 "/\" v2)) = (v1 "\/" (v0 "/\" v0)) "\/" (v2 "/\" (v3 "\/" v0))

proof

let v0, v1, v2, v3 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v1 "\/" v2) "/\" (v3 "\/" v1)) = v0 "\/" (v1 "\/" (v3 "/\" v2)) by A223;
hence v0 "\/" (v1 "\/" (v3 "/\" v2)) = (v1 "\/" (v0 "/\" v0)) "\/" (v2 "/\" (v3 "\/" v0)) by A2706; :: thesis:

end;

A2711: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v1 "\/" (v2 "/\" v3)) = v1 "\/" ((v0 "/\" v0) "\/" (v3 "/\" (v2 "\/" v0)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" (v0 "/\" v0)) "\/" (v3 "/\" (v2 "\/" v0)) = v1 "\/" ((v0 "/\" v0) "\/" (v3 "/\" (v2 "\/" v0))) by A181;
hence v0 "\/" (v1 "\/" (v2 "/\" v3)) = v1 "\/" ((v0 "/\" v0) "\/" (v3 "/\" (v2 "\/" v0))) by A2708; :: thesis:

end;

A2713: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v1 "\/" (v2 "/\" v3)) = v1 "\/" (v0 "\/" (v3 "/\" (v2 "\/" v0)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v0) "\/" (v3 "/\" (v2 "\/" v0)) = v0 "\/" (v3 "/\" (v2 "\/" v0)) ;
hence v0 "\/" (v1 "\/" (v2 "/\" v3)) = v1 "\/" (v0 "\/" (v3 "/\" (v2 "\/" v0))) by A2711; :: thesis:

end;

A2715: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v1 "\/" (v2 "/\" v3)) = v0 "\/" ((v3 "/\" (v2 "\/" v0)) "\/" v1)

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "\/" ((v3 "/\" (v2 "\/" v0)) "\/" v1) = v1 "\/" (v0 "\/" (v3 "/\" (v2 "\/" v0))) by A8;
hence v0 "\/" (v1 "\/" (v2 "/\" v3)) = v0 "\/" ((v3 "/\" (v2 "\/" v0)) "\/" v1) by A2713; :: thesis:

end;

A2721: for v0, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "\/" (v0 "/\" v0)) = v1 "\/" (v0 "/\" v0)

proof

let v0, v1 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v1 "\/" (v0 "/\" v0)) = v0 "\/" (v1 "/\" v1) by A2397;
hence v0 "\/" (v1 "\/" (v0 "/\" v0)) = v1 "\/" (v0 "/\" v0) ; :: thesis:

end;

A2773: for v2, v1, v0 being Element of (BA2TBAA B) holds (v1 "/\" v0) "\/" (v2 "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" v1))

proof

let v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "\/" v1)) "\/" (v2 "/\" (v0 "\/" v1)) = (v1 "/\" v0) "\/" (v2 "/\" (v0 "\/" v1)) ;
hence (v1 "/\" v0) "\/" (v2 "/\" (v0 "\/" v1)) = (v0 "\/" v1) "/\" (v2 "\/" (v0 "/\" v1)) by A2680; :: thesis:

end;

A2780: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "\/" c4) "/\" (c2 "\/" (c3 "/\" c4))))) by A2773, A2677;
A2782: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "/\" c4) "\/" (c2 "/\" (c3 "\/" c4))))) by A2773, A2780;
A2784: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" ((c3 "/\" c4) "\/" (c3 "\/" c4)))) by A2492, A2782;
A2788: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" (c3 "\/" (c4 "\/" (c3 "/\" c4))))) by A181, A2784;
A2790: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = (c2 "\/" (c3 "/\" c4)) "/\" (c1 "\/" (c2 "/\" (c3 "\/" (c4 "/\" c4)))) by A2533, A2788;
A2795: for v101, v102, v2, v3, v1, v0 being Element of (BA2TBAA B) holds ((v0 "/\" (v1 "/\" v2)) "\/" v101) "/\" (v102 "\/" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = (v0 "/\" (v1 "/\" v2)) "\/" (v101 "/\" (v102 "\/" (v2 "/\" v3)))

proof

let v101, v102, v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v2)) "\/" (v2 "/\" v3) = v2 "/\" (v3 "\/" (v0 "/\" v1)) by A131;
hence ((v0 "/\" (v1 "/\" v2)) "\/" v101) "/\" (v102 "\/" (v2 "/\" (v3 "\/" (v0 "/\" v1)))) = (v0 "/\" (v1 "/\" v2)) "\/" (v101 "/\" (v102 "\/" (v2 "/\" v3))) by A270; :: thesis:

end;

A2802: for v103, v102, v101 being Element of (BA2TBAA B) holds (v101 "\/" v102) "/\" (v102 "\/" v103) = v102 "\/" (v103 "/\" ((v101 "\/" v102) "\/" v101))

proof

let v103, v102, v101 be Element of (BA2TBAA B); :: thesis:
((v101 "\/" v102) "\/" (v101 "\/" v102)) "/\" (v102 "\/" v103) = (v101 "\/" v102) "/\" (v102 "\/" v103) ;
hence (v101 "\/" v102) "/\" (v102 "\/" v103) = v102 "\/" (v103 "/\" ((v101 "\/" v102) "\/" v101)) by A117; :: thesis:

end;

A2805: for v1, v2, v0 being Element of (BA2TBAA B) holds v1 "\/" (v0 "/\" v2) = v1 "\/" (v2 "/\" ((v0 "\/" v1) "\/" v0))

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" v1) "/\" (v1 "\/" v2) = v1 "\/" (v0 "/\" v2) by A4;
hence v1 "\/" (v0 "/\" v2) = v1 "\/" (v2 "/\" ((v0 "\/" v1) "\/" v0)) by A2802; :: thesis:

end;

A2810: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" v2) = v0 "\/" (v2 "/\" (v1 "\/" v0))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "/\" (v1 "\/" (v1 "\/" v0)) = v2 "/\" (v1 "\/" v0) by A2435;
hence v0 "\/" (v1 "/\" v2) = v0 "\/" (v2 "/\" (v1 "\/" v0)) by A2805; :: thesis:

end;

A2815: for v1, v2, v100, v102, v101 being Element of (BA2TBAA B) holds (v100 "/\" (v101 "/\" v102)) "\/" (v101 "/\" (v1 "\/" v2)) = v101 "/\" ((v1 "\/" (v101 "/\" v2)) "\/" (v100 "/\" v102))

proof

let v1, v2, v100, v102, v101 be Element of (BA2TBAA B); :: thesis:
v101 "/\" (v1 "\/" (v101 "/\" v2)) = v101 "/\" (v1 "\/" v2) by A2492;
hence (v100 "/\" (v101 "/\" v102)) "\/" (v101 "/\" (v1 "\/" v2)) = v101 "/\" ((v1 "\/" (v101 "/\" v2)) "\/" (v100 "/\" v102)) by A123; :: thesis:

end;

A2818: for v1, v0, v2, v4, v3 being Element of (BA2TBAA B) holds v1 "/\" ((v3 "\/" v4) "\/" (v0 "/\" v2)) = v1 "/\" ((v3 "\/" (v1 "/\" v4)) "\/" (v0 "/\" v2))

proof

let v1, v0, v2, v4, v3 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" v2)) "\/" (v1 "/\" (v3 "\/" v4)) = v1 "/\" ((v3 "\/" v4) "\/" (v0 "/\" v2)) by A123;
hence v1 "/\" ((v3 "\/" v4) "\/" (v0 "/\" v2)) = v1 "/\" ((v3 "\/" (v1 "/\" v4)) "\/" (v0 "/\" v2)) by A2815; :: thesis:

end;

A2821: for v0, v1, v2, v4, v3 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" v4))) = v0 "/\" ((v1 "\/" (v0 "/\" v2)) "\/" (v3 "/\" v4))

proof

let v0, v1, v2, v4, v3 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" v2) "\/" (v3 "/\" v4) = v1 "\/" (v2 "\/" (v3 "/\" v4)) by A181;
hence v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" v4))) = v0 "/\" ((v1 "\/" (v0 "/\" v2)) "\/" (v3 "/\" v4)) by A2818; :: thesis:

end;

A2823: for v0, v1, v2, v4, v3 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" v4))) = v0 "/\" (v1 "\/" ((v0 "/\" v2) "\/" (v3 "/\" v4)))

proof

let v0, v1, v2, v4, v3 be Element of (BA2TBAA B); :: thesis:
(v1 "\/" (v0 "/\" v2)) "\/" (v3 "/\" v4) = v1 "\/" ((v0 "/\" v2) "\/" (v3 "/\" v4)) by A181;
hence v0 "/\" (v1 "\/" (v2 "\/" (v3 "/\" v4))) = v0 "/\" (v1 "\/" ((v0 "/\" v2) "\/" (v3 "/\" v4))) by A2821; :: thesis:

end;

A2838: for v102, v100, v1 being Element of (BA2TBAA B) holds (v1 "/\" (v100 "\/" v100)) "\/" (v100 "/\" v102) = v100 "/\" ((v1 "/\" (v100 "\/" v100)) "\/" v102)

proof

let v102, v100, v1 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v1 "/\" (v100 "\/" v100)) = v1 "/\" (v100 "\/" v100) by A2618;
hence (v1 "/\" (v100 "\/" v100)) "\/" (v100 "/\" v102) = v100 "/\" ((v1 "/\" (v100 "\/" v100)) "\/" v102) by A6; :: thesis:

end;

A2847: for v1, v2, v0 being Element of (BA2TBAA B) holds v1 "/\" (v0 "\/" v2) = v1 "/\" ((v0 "/\" (v1 "\/" v1)) "\/" v2)

proof

let v1, v2, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v1 "/\" v2) = v1 "/\" (v0 "\/" v2) by A6;
hence v1 "/\" (v0 "\/" v2) = v1 "/\" ((v0 "/\" (v1 "\/" v1)) "\/" v2) by A2838; :: thesis:

end;

A2852: for v0, v2, v1 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" v2) = v0 "/\" (v2 "\/" (v0 "/\" v1))

proof

let v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v2 "\/" (v1 "/\" (v0 "\/" v0)) = v2 "\/" (v0 "/\" v1) ;
hence v0 "/\" (v1 "\/" v2) = v0 "/\" (v2 "\/" (v0 "/\" v1)) by A2847; :: thesis:

end;

A2859: for v103, v100, v101, v1 being Element of (BA2TBAA B) holds (v100 "/\" (v1 "/\" (v101 "\/" v101))) "\/" (v101 "/\" v103) = v101 "/\" (v103 "\/" (v100 "/\" (v1 "/\" (v101 "\/" v101))))

proof

let v103, v100, v101, v1 be Element of (BA2TBAA B); :: thesis:
v101 "/\" (v1 "/\" (v101 "\/" v101)) = v1 "/\" (v101 "\/" v101) by A2618;
hence (v100 "/\" (v1 "/\" (v101 "\/" v101))) "\/" (v101 "/\" v103) = v101 "/\" (v103 "\/" (v100 "/\" (v1 "/\" (v101 "\/" v101)))) by A123; :: thesis:

end;

A2862: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v2 "/\" (v3 "\/" (v0 "/\" v1)) = v2 "/\" (v3 "\/" (v0 "/\" (v1 "/\" (v2 "\/" v2))))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "/\" (v2 "\/" v2))) "\/" (v2 "/\" v3) = v2 "/\" (v3 "\/" (v0 "/\" v1)) by A123;
hence v2 "/\" (v3 "\/" (v0 "/\" v1)) = v2 "/\" (v3 "\/" (v0 "/\" (v1 "/\" (v2 "\/" v2)))) by A2859; :: thesis:

end;

A2865: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "/\" v3)) = v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v3)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v1 "\/" (v2 "/\" (v3 "/\" (v0 "\/" v0))) = v1 "\/" (v0 "/\" (v2 "/\" v3)) by A14;
hence v0 "/\" (v1 "\/" (v2 "/\" v3)) = v0 "/\" (v1 "\/" (v0 "/\" (v2 "/\" v3))) by A2862; :: thesis:

end;

A2867: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "/\" v3)) = v0 "/\" (v1 "\/" (v3 "/\" (v0 "/\" v2)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "/\" (v2 "/\" v3) = v3 "/\" (v0 "/\" v2) by A14;
hence v0 "/\" (v1 "\/" (v2 "/\" v3)) = v0 "/\" (v1 "\/" (v3 "/\" (v0 "/\" v2))) by A2865; :: thesis:

end;

A2886: for v3, v2, v1, v0 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v2 "\/" (v0 "/\" v1))) = (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3))

proof

let v3, v2, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v2 "\/" (v0 "/\" v1)) "/\" (v0 "\/" (v3 "\/" (v0 "/\" v1))) = (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) by A305;
hence (v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v2 "\/" (v0 "/\" v1))) = (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) by A511; :: thesis:

end;

A2889: for v103, v100, v101, v1 being Element of (BA2TBAA B) holds (v100 "\/" (v1 "\/" (v101 "/\" v101))) "/\" (v101 "\/" v103) = v101 "\/" (v103 "/\" (v100 "\/" (v1 "\/" (v101 "/\" v101))))

proof

let v103, v100, v101, v1 be Element of (BA2TBAA B); :: thesis:
v101 "\/" (v1 "\/" (v101 "/\" v101)) = v1 "\/" (v101 "/\" v101) by A2721;
hence (v100 "\/" (v1 "\/" (v101 "/\" v101))) "/\" (v101 "\/" v103) = v101 "\/" (v103 "/\" (v100 "\/" (v1 "\/" (v101 "/\" v101)))) by A109; :: thesis:

end;

A2892: for v2, v3, v1, v0 being Element of (BA2TBAA B) holds v2 "\/" (v3 "/\" (v0 "\/" v1)) = v2 "\/" (v3 "/\" (v0 "\/" (v1 "\/" (v2 "/\" v2))))

proof

let v2, v3, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" (v2 "/\" v2))) "/\" (v2 "\/" v3) = v2 "\/" (v3 "/\" (v0 "\/" v1)) by A109;
hence v2 "\/" (v3 "/\" (v0 "\/" v1)) = v2 "\/" (v3 "/\" (v0 "\/" (v1 "\/" (v2 "/\" v2)))) by A2889; :: thesis:

end;

A2895: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v2 "\/" v3)) = v0 "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v2 "\/" (v3 "\/" (v0 "/\" v0))) = v1 "/\" (v0 "\/" (v2 "\/" v3)) by A2565;
hence v0 "\/" (v1 "/\" (v2 "\/" v3)) = v0 "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))) by A2892; :: thesis:

end;

A2897: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "\/" (v1 "/\" (v2 "\/" v3)) = v0 "\/" (v1 "/\" (v3 "\/" (v0 "\/" v2)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v2 "\/" v3) = v3 "\/" (v0 "\/" v2) by A8;
hence v0 "\/" (v1 "/\" (v2 "\/" v3)) = v0 "\/" (v1 "/\" (v3 "\/" (v0 "\/" v2))) by A2895; :: thesis:

end;

A2907: for v102, v1, v100, v2 being Element of (BA2TBAA B) holds (v100 "/\" (v2 "\/" v1)) "\/" ((v1 "\/" (v2 "/\" v100)) "/\" v102) = (v1 "\/" (v2 "/\" v100)) "/\" (v100 "\/" v102)

proof

let v102, v1, v100, v2 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v1 "\/" (v2 "/\" v100)) = v100 "/\" (v2 "\/" v1) by A2852;
hence (v100 "/\" (v2 "\/" v1)) "\/" ((v1 "\/" (v2 "/\" v100)) "/\" v102) = (v1 "\/" (v2 "/\" v100)) "/\" (v100 "\/" v102) by A6; :: thesis:

end;

A2914: for v1, v2, v3, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) = (v2 "\/" (v1 "/\" v0)) "/\" (v0 "\/" v3)

proof

let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" (v1 "\/" v2)) "\/" (v3 "/\" (v2 "\/" (v0 "/\" v1))) = (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) by A2886;
hence (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) = (v2 "\/" (v1 "/\" v0)) "/\" (v0 "\/" v3) by A2907; :: thesis:

end;

A2921: for v102, v101, v1, v0 being Element of (BA2TBAA B) holds (v102 "/\" v101) "\/" (v101 "/\" (v0 "\/" v1)) = v101 "/\" ((v0 "\/" (v1 "\/" (v102 "/\" v101))) "\/" ((v0 "\/" (v1 "\/" (v102 "/\" v101))) "/\" v102))

proof

let v102, v101, v1, v0 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "\/" (v102 "/\" v101))) "/\" (v101 "\/" (v102 "/\" v101)) = (v102 "/\" v101) "\/" (v101 "/\" (v0 "\/" v1)) by A346;
hence (v102 "/\" v101) "\/" (v101 "/\" (v0 "\/" v1)) = v101 "/\" ((v0 "\/" (v1 "\/" (v102 "/\" v101))) "\/" ((v0 "\/" (v1 "\/" (v102 "/\" v101))) "/\" v102)) by A1005; :: thesis:

end;

A2924: for v1, v0, v3, v2 being Element of (BA2TBAA B) holds v1 "/\" (v0 "\/" (v2 "\/" v3)) = v1 "/\" ((v2 "\/" (v3 "\/" (v0 "/\" v1))) "\/" ((v2 "\/" (v3 "\/" (v0 "/\" v1))) "/\" v0))

proof

let v1, v0, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "/\" v1) "\/" (v1 "/\" (v2 "\/" v3)) = v1 "/\" (v0 "\/" (v2 "\/" v3)) by A6;
hence v1 "/\" (v0 "\/" (v2 "\/" v3)) = v1 "/\" ((v2 "\/" (v3 "\/" (v0 "/\" v1))) "\/" ((v2 "\/" (v3 "\/" (v0 "/\" v1))) "/\" v0)) by A2921; :: thesis:

end;

A2929: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" ((v2 "\/" (v3 "\/" (v1 "/\" v0))) "\/" (v1 "/\" (v2 "\/" (v3 "\/" v0))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v2 "\/" (v3 "\/" (v1 "/\" v0))) = v1 "/\" (v2 "\/" (v3 "\/" v0)) by A2583;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" ((v2 "\/" (v3 "\/" (v1 "/\" v0))) "\/" (v1 "/\" (v2 "\/" (v3 "\/" v0)))) by A2924; :: thesis:

end;

A2933: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" ((v2 "\/" (v3 "\/" (v1 "/\" v0))) "\/" (v1 "/\" (v0 "\/" (v3 "\/" v2))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v0 "\/" (v3 "\/" v2) = v2 "\/" (v0 "\/" v3) by A8;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" ((v2 "\/" (v3 "\/" (v1 "/\" v0))) "\/" (v1 "/\" (v0 "\/" (v3 "\/" v2)))) by A2929; :: thesis:

end;

A2937: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" ((v3 "\/" (v1 "/\" v0)) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3)))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v2 "\/" (v3 "\/" (v1 "/\" v0))) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))) = v2 "\/" ((v3 "\/" (v1 "/\" v0)) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3)))) by A181;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" ((v3 "\/" (v1 "/\" v0)) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))))) by A2933; :: thesis:

end;

A2939: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" ((v1 "/\" v0) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v3 "\/" (v1 "/\" v0)) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))) = v3 "\/" ((v1 "/\" v0) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3)))) by A181;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" ((v1 "/\" v0) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3)))))) by A2937; :: thesis:

end;

A2941: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" (v0 "\/" (v2 "\/" v3))))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v1 "/\" v0) "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))) = v1 "/\" (v0 "\/" (v0 "\/" (v2 "\/" v3))) by A6;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" (v0 "\/" (v2 "\/" v3)))))) by A2939; :: thesis:

end;

A2943: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3)))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v1 "/\" (v0 "\/" (v0 "\/" (v2 "\/" v3))) = v1 "/\" (v0 "\/" (v2 "\/" v3)) by A2435;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))))) by A2941; :: thesis:

end;

A2945: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" v2))))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v3 "\/" (v1 "/\" (v0 "\/" (v2 "\/" v3))) = v3 "\/" (v1 "/\" (v0 "\/" v2)) by A2897;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" v2)))) by A2943; :: thesis:

end;

A2947: for v0, v1, v3, v2 being Element of (BA2TBAA B) holds v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1)))

proof

let v0, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v2 "\/" (v3 "\/" (v1 "/\" (v0 "\/" v2))) = v2 "\/" (v3 "\/" (v0 "/\" v1)) by A2715;
hence v0 "/\" (v1 "\/" (v2 "\/" v3)) = v0 "/\" (v2 "\/" (v3 "\/" (v0 "/\" v1))) by A2945; :: thesis:

end;

A2969: not (c2 "\/" (c1 "/\" (c3 "/\" c4))) "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = (c2 "/\" (c3 "\/" c4)) "\/" (c1 "/\" (c2 "\/" (c3 "/\" c4))) by A2914, A2790;
A2972: for v101, v102, v1, v3, v2 being Element of (BA2TBAA B) holds (v1 "\/" (v2 "/\" (v3 "/\" v102))) "/\" (v101 "\/" (v102 "/\" (v1 "\/" (v2 "/\" v3)))) = (v1 "\/" (v2 "/\" (v3 "/\" v102))) "/\" (v102 "\/" v101)

proof

let v101, v102, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
v102 "/\" (v1 "\/" (v2 "/\" (v3 "/\" v102))) = v102 "/\" (v1 "\/" (v2 "/\" v3)) by A2867;
hence (v1 "\/" (v2 "/\" (v3 "/\" v102))) "/\" (v101 "\/" (v102 "/\" (v1 "\/" (v2 "/\" v3)))) = (v1 "\/" (v2 "/\" (v3 "/\" v102))) "/\" (v102 "\/" v101) by A2852; :: thesis:

end;

A2975: for v0, v4, v1, v3, v2 being Element of (BA2TBAA B) holds (v1 "/\" (v2 "/\" v3)) "\/" (v0 "/\" (v4 "\/" (v3 "/\" v0))) = (v0 "\/" (v1 "/\" (v2 "/\" v3))) "/\" (v3 "\/" v4)

proof

let v0, v4, v1, v3, v2 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "/\" (v2 "/\" v3))) "/\" (v4 "\/" (v3 "/\" (v0 "\/" (v1 "/\" v2)))) = (v1 "/\" (v2 "/\" v3)) "\/" (v0 "/\" (v4 "\/" (v3 "/\" v0))) by A2795;
hence (v1 "/\" (v2 "/\" v3)) "\/" (v0 "/\" (v4 "\/" (v3 "/\" v0))) = (v0 "\/" (v1 "/\" (v2 "/\" v3))) "/\" (v3 "\/" v4) by A2972; :: thesis:

end;

A2980: for v4, v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" (v1 "/\" v2)) "\/" (v3 "/\" (v4 "\/" v2)) = (v3 "\/" (v0 "/\" (v1 "/\" v2))) "/\" (v2 "\/" v4)

proof

let v4, v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
v3 "/\" (v4 "\/" (v3 "/\" v2)) = v3 "/\" (v4 "\/" v2) by A2492;
hence (v0 "/\" (v1 "/\" v2)) "\/" (v3 "/\" (v4 "\/" v2)) = (v3 "\/" (v0 "/\" (v1 "/\" v2))) "/\" (v2 "\/" v4) by A2975; :: thesis:

end;

A2986: not (c1 "/\" (c3 "/\" c4)) "\/" (c2 "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3))))) = (c2 "/\" (c3 "\/" c4)) "\/" (c1 "/\" (c2 "\/" (c3 "/\" c4))) by A2980, A2969;
A2987: c2 "/\" (c4 "\/" ((c2 "/\" c3) "\/" (c1 "/\" (c2 "\/" c3)))) = c2 "/\" (c4 "\/" (c3 "\/" (c1 "/\" (c2 "\/" c3)))) by A2823;
A2992: not (c1 "/\" (c3 "/\" c4)) "\/" (c2 "/\" (c4 "\/" (c3 "\/" (c1 "/\" c2)))) = (c2 "/\" (c3 "\/" c4)) "\/" (c1 "/\" (c2 "\/" (c3 "/\" c4))) by A2810, A2987, A2986;
A2998: not (c1 "/\" (c3 "/\" c4)) "\/" (c2 "/\" (c1 "\/" (c3 "\/" c4))) = (c2 "/\" (c3 "\/" c4)) "\/" (c1 "/\" (c2 "\/" (c3 "/\" c4))) by A2947, A2992;
A3002: for v2, v100, v102, v101 being Element of (BA2TBAA B) holds (v100 "\/" (v101 "/\" v102)) "/\" (v101 "\/" (v100 "/\" v2)) = (v101 "/\" v102) "\/" (v100 "/\" (v101 "\/" v2))

proof

let v2, v100, v102, v101 be Element of (BA2TBAA B); :: thesis:
v100 "/\" (v101 "\/" (v100 "/\" v2)) = v100 "/\" (v101 "\/" v2) by A2492;
hence (v100 "\/" (v101 "/\" v102)) "/\" (v101 "\/" (v100 "/\" v2)) = (v101 "/\" v102) "\/" (v100 "/\" (v101 "\/" v2)) by A2914; :: thesis:

end;

A3005: for v3, v0, v2, v1 being Element of (BA2TBAA B) holds (v0 "/\" v3) "\/" (v1 "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v1 "\/" v3))

proof

let v3, v0, v2, v1 be Element of (BA2TBAA B); :: thesis:
(v0 "\/" (v1 "/\" v2)) "/\" (v1 "\/" (v0 "/\" v3)) = (v0 "/\" v3) "\/" (v1 "/\" (v0 "\/" (v1 "/\" v2))) by A2914;
hence (v0 "/\" v3) "\/" (v1 "/\" (v0 "\/" (v1 "/\" v2))) = (v1 "/\" v2) "\/" (v0 "/\" (v1 "\/" v3)) by A3002; :: thesis:

end;

for v1, v2, v3, v0 being Element of (BA2TBAA B) holds (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) = (v2 "/\" v3) "\/" (v0 "/\" (v2 "\/" v1))

proof

let v1, v2, v3, v0 be Element of (BA2TBAA B); :: thesis:
v2 "/\" (v0 "\/" (v2 "/\" v3)) = v2 "/\" (v0 "\/" v3) by A2492;
hence (v0 "/\" v1) "\/" (v2 "/\" (v0 "\/" v3)) = (v2 "/\" v3) "\/" (v0 "/\" (v2 "\/" v1)) by A3005; :: thesis:

end;

hence contradiction by A2998; :: thesis: