proposition: Lemma binds_eq_indom_read : forall A `{Inhab B} (M:map A B) x v, binds M x v = (x \indom M /\ M[x] = v).
proof: Proof. Proof using. intros. simpl. unfold dom_impl, read_impl, binds_impl. extens. rew_set. iff R (N&R). rewrite R. split~. congruence. destruct (M x). subst~. false. Qed.
imports: TLC(LibTactics LibLogic LibReflect LibOption LibRelation LibLogic LibOperation LibEpsilon LibMonoid LibSet)