proposition: Lemma Exists_cons_inv : forall P l x, Exists P (x::l) -> P x \/ Exists P l.
proof: Proof. Proof using. introv H. rewrite* Exists_cons_eq in H. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)