proposition: Lemma binds_push_neq_inv : forall x1 x2 v1 v2 E, binds x1 v1 (E & x2 ~ v2) -> x1 <> x2 -> binds x1 v1 E.
proof: Proof. Proof using. introv H. forwards [|]: binds_push_inv H; auto_false*. Qed.
imports: TLC(LibTactics LibOption LibList LibProd LibLogic LibReflect)