Definition restrict_env_comp  {key: Type}{A: Type}{KE: EqDec key} (ids: list key) (rho:env key A) : env key A:=
  mk_env _ (restrict_env_comp'_finite ids rho).

Lemma restrict_env_rev {key: Type}{A: Type}{KE: EqDec key}: forall ids, @restrict_env key A _ (rev ids) = restrict_env ids.