Section RelaxedExpansion.
Variables A X Y: Type.
Variable TX: reduction_t A X.
Variable TY: reduction_t A Y.
Variable B: relation X.
Hypothesis HB: wexpansion1 TX TX B.
(** Silent case *)
Let wexpansion1_ctrl_t:
forall R, evolve_t TX TY R (comp (star B) R) -> simulation_t TX TY (comp (star B) R).

(** Lemma 3.10 *)
Theorem wexpansion1_ctrl: wexpansion1 TX TX B -> controlled TX TY B.