
theorem
  for x,y,z being set st z <> [<*x,y*>, xor2c] for s being State of
GFA2AdderCirc(x,y,z) for a1a2,a1,a2,a3 being Element of BOOLEAN st a1a2 = s.[<*
  x,y*>,xor2c] & a1 = s.x & a2 = s.y & a3 = s.z holds (Following s).
  GFA2AdderOutput(x,y,z) = a1a2 'xor' 'not' a3
proof
  set f = xor2c;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f];
  set O1 = GFA1AdderOutput(x,y,z);
  set O2 = GFA2AdderOutput(x,y,z);
  set A1 = GFA1AdderCirc(x,y,z);
  set A2 = GFA2AdderCirc(x,y,z);
  A2 = A1 & O2 = O1;
  hence thesis by A1,Th60;
end;
