proposition: Lemma Exists_nil_inv : forall P, Exists P nil -> False.
proof: Proof. Proof using. introv H. rewrite* Exists_nil_eq in H. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)