
theorem
  for x,y,z being set st z <> [<*x,y*>,xor2] & x <> [<*y,z*>,nor2] & y
<> [<*z,x*>,nor2] & z <> [<*x,y*>,nor2] holds x in InputVertices BitGFA3Str(x
,y,z) & y in InputVertices BitGFA3Str(x,y,z) & z in InputVertices BitGFA3Str(x,
  y,z)
proof
  set f1 = nor2, f2 = nor2, f3 = nor2;
  set f0 = xor2;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f0] & x <> [<*y,z*>,f2] & y <> [<*z,x*>,f3] & z <> [<*
  x,y*>,f1];
  set S = BitGFA3Str(x,y,z);
  InputVertices S = {x,y,z} by A1,Th129;
  hence thesis by ENUMSET1:def 1;
end;
