proposition: Lemma Exists_take_inv : forall P n l, Exists P (take n l) -> Exists P l.
proof: Proof. Proof using. introv E. forwards (q&K): take_is_prefix n l. rewrite K. rewrite* Exists_app_eq. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)