proposition: Lemma mem_remove_inv : forall x a l, mem x (remove a l) -> mem x l /\ x <> a.
proof: Proof. Proof using. introv E. rewrite* mem_remove_eq in E. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)