
theorem
  for x,y,z being set st z <> [<*x,y*>, xor2c] for s being State of
GFA2AdderCirc(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*>,xor2c] = a1 'xor' 'not' a2 & (
  Following s).x = a1 & (Following s).y = a2 & (Following s).z = a3
proof
  set f = xor2c;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f];
  set A1 = GFA1AdderCirc(x,y,z);
  GFA2AdderCirc(x,y,z) = A1;
  hence thesis by A1,Th59;
end;
