proposition: Lemma subvars_app_remove_nvars_r : forall vs1 vs2 vs, subvars vs (vs1 ++ remove_nvars vs1 vs2) <=> subvars vs (vs1 ++ vs2).
proof: Proof. sp; alltrewrite subvars_eq; unfold subset; split; sp. apply_in_hyp p; alltrewrite in_app_iff; sp. alltrewrite in_remove_nvars; sp. apply_in_hyp p; alltrewrite in_app_iff; sp. alltrewrite in_remove_nvars; sp. destruct (in_nvar_list_dec x vs1); sp. Qed.
imports: list Omega