Definition var_env''le (ve1 ve2 : var_env'') :=
  forall x : ad, in_dom _ x ve1 = true -> in_dom _ x ve2 = true.

Lemma incl_eq : forall (U : Type) (A B : Ensemble U) (n : nat), Included _ A B -> cardinal _ A n -> cardinal _ B n -> Included _ B A.