reserve x,y,z,c for object,
  f for Function of 2-tuples_on BOOLEAN, BOOLEAN;

theorem
  for f being Function of 3-tuples_on BOOLEAN, BOOLEAN for s being State
of 1GateCircuit(x,y,z,f) holds (Following s).[<*x,y,z*>, f] = f.<*s.x, s.y, s.z
  *> & (Following s).x = s.x & (Following s).y = s.y & (Following s).z = s.z
by Th52;
