proposition: Theorem update_neq : forall (X:Type) v x1 x2 (m : partial_map X), x2 <> x1 -> (update m x2 v) x1 = m x1.
proof: Proof. intros X v x1 x2 m H. unfold update. rewrite t_update_neq. reflexivity. apply H. Qed.
imports: Coq.Arith.Arith Coq.Bool.Bool Coq.Strings.String Coq.Logic.FunctionalExtensionality