set f1 = nor2 ;
set f2 = nor2 ;
set f3 = nor2 ;
set f0 = xor2 ;
let x, y, z be set ; :: thesis: ( z <> [<*x,y*>,xor2] & x <> [<*y,z*>,nor2] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,nor2] implies ( x in InputVertices (BitGFA3Str (x,y,z)) & y in InputVertices (BitGFA3Str (x,y,z)) & z in InputVertices (BitGFA3Str (x,y,z)) ) )
assume A1: ( z <> [<*x,y*>,xor2] & x <> [<*y,z*>,nor2] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,nor2] ) ; :: thesis: ( x in InputVertices (BitGFA3Str (x,y,z)) & y in InputVertices (BitGFA3Str (x,y,z)) & z in InputVertices (BitGFA3Str (x,y,z)) )
set S = BitGFA3Str (x,y,z);
InputVertices (BitGFA3Str (x,y,z)) = {x,y,z} by A1, Th129;
hence ( x in InputVertices (BitGFA3Str (x,y,z)) & y in InputVertices (BitGFA3Str (x,y,z)) & z in InputVertices (BitGFA3Str (x,y,z)) ) by ENUMSET1:def 1; :: thesis: verum