proposition: Lemma binds_push_neq : forall x1 x2 v1 v2 E, binds x1 v1 E -> x1 <> x2 -> binds x1 v1 (E & x2 ~ v2).
proof: Proof. Proof using. introv H N. unfolds binds. rewrite get_push. case_if~. Qed.
imports: TLC(LibTactics LibOption LibList LibProd LibLogic LibReflect)