
theorem
  for x,y,z being set st z <> [<*x,y*>, xor2] for s being State of
GFA3AdderCirc(x,y,z) for a1,a2,a3 being Element of BOOLEAN st a1 = s.x & a2 = s
.y & a3 = s.z holds (Following s).[<*x,y*>,xor2] = a1 'xor' a2 & (Following s).
  x = a1 & (Following s).y = a2 & (Following s).z = a3
proof
  set f = xor2;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f];
  set A0 = GFA0AdderCirc(x,y,z);
  set A3 = GFA3AdderCirc(x,y,z);
  A3 = A0;
  hence thesis by A1,Th28;
end;
