proposition: Lemma memberb_din : forall (S T : Type) (deq : Deq S) (v : S) (lv : list S) (ct cf : T), (if memberb deq v lv then ct else cf) = (if in_deq _ deq v lv then ct else cf).
proof: Proof. intros. cases_if as Hb; auto; cases_if_sum Hd ; auto; subst. apply assert_memberb in Hb. sp. rw <- (@assert_memberb S deq) in Hd. rewrite Hd in Hb. sp. Qed.
imports: UsefulTypes bin_rels Omega