proposition: Lemma update_eq : forall A (m: partial_map A) x v, (update m x v) x = Some v.
proof: Proof. intros. unfold update. rewrite t_update_eq. reflexivity. Qed.
imports: Coq.Arith.Arith Coq.Bool.Bool Coq.Strings.String Coq.Logic.FunctionalExtensionality