set f1 = and2a ;
set f2 = and2c ;
set f3 = nor2 ;
set f0 = xor2c ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2c] & x <> [<*y,z*>,and2c] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,and2a] implies ( x in InputVertices (BitGFA2Str (x,y,z)) & y in InputVertices (BitGFA2Str (x,y,z)) & z in InputVertices (BitGFA2Str (x,y,z)) ) )
assume A1: ( z <> [<*x,y*>,xor2c] & x <> [<*y,z*>,and2c] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,and2a] ) ; :: thesis: ( x in InputVertices (BitGFA2Str (x,y,z)) & y in InputVertices (BitGFA2Str (x,y,z)) & z in InputVertices (BitGFA2Str (x,y,z)) )
set S = BitGFA2Str (x,y,z);
InputVertices (BitGFA2Str (x,y,z)) = {x,y,z} by A1, Th97;
hence ( x in InputVertices (BitGFA2Str (x,y,z)) & y in InputVertices (BitGFA2Str (x,y,z)) & z in InputVertices (BitGFA2Str (x,y,z)) ) by ENUMSET1:def 1; :: thesis: verum