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

Lemma decreasing_ens_seq :
forall (U : Type) (n : nat) (f : nat -> Ensemble U),
cardinal _ (f 0) n ->
(forall k : nat, Finite _ (f k)) ->
(forall k : nat, Included _ (f (S k)) (f k)) ->
exists m : nat,
(exists c : nat, m <= n /\ cardinal _ (f m) c /\ cardinal _ (f (S m)) c).