Section WeakMonotonicCorrect.
Variable F: function X Y.
Hypothesis HF: wmonotonic TX TY F.
Variable R: relation2 X Y.
Hypothesis HRt: simulation_t TX TY R.
Hypothesis HRa: evolve_a TX TY R (F R).
(** first induction predicate *)
Let silent: forall n, simulation_t TX TY (UExp F R n).
(** second induction predicate *)
Let visible: forall n, evolve_a TX TY (UExp F R n) (UExp F R (S n)).

(** Proposition 2.2 *)
Theorem wmonotonic_correct: simulation TX TY (UIter F R).