
theorem
  for x,y,z being set st z <> [<*x,y*>, xor2c] holds x in InputVertices
  GFA2AdderStr(x,y,z) & y in InputVertices GFA2AdderStr(x,y,z) & z in
  InputVertices GFA2AdderStr(x,y,z)
proof
  set f = xor2c;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f];
  set S1 = GFA1AdderStr(x,y,z);
  GFA2AdderStr(x,y,z) = S1;
  hence thesis by A1,Th58;
end;
