
theorem
  for x,y,z being set st z <> [<*x,y*>,xor2c] & x <> [<*y,z*>,and2a] & y
<> [<*z,x*>,and2] & z <> [<*x,y*>,and2c] holds x in InputVertices BitGFA1Str(x,
y,z) & y in InputVertices BitGFA1Str(x,y,z) & z in InputVertices BitGFA1Str(x,y
  ,z)
proof
  set f1 = and2c, f2 = and2a, f3 = and2;
  set f0 = xor2c;
  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 = BitGFA1Str(x,y,z);
  InputVertices S = {x,y,z} by A1,Th65;
  hence thesis by ENUMSET1:def 1;
end;
