theorem Th81:
  for u being Function of D,D holds
  (F*(id D,u)).(d1,d2) = F.(d1,u.d2) & (F*(u,id D)).(d1,d2) = F.(u.d1,d2)
proof
  let u be Function of D,D;
  (id D).d1 = d1 & (id D).d2 = d2;
  hence thesis by Th80;
end;
