
theorem Th27:
  for x,y,z being set st z <> [<*x,y*>, xor2] holds x in
InputVertices GFA0AdderStr(x,y,z) & y in InputVertices GFA0AdderStr(x,y,z) & z
  in InputVertices GFA0AdderStr(x,y,z)
proof
  set f = xor2;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f];
  set S = GFA0AdderStr(x,y,z);
  InputVertices S = {x,y,z} by A1,FACIRC_1:57;
  hence thesis by ENUMSET1:def 1;
end;
