proposition: Lemma nth_Exists : forall {IA:Inhab A} P n l, P (nth n l) -> n < length l -> Exists P l.
proof: Proof. Proof using. introv H N. applys* Nth_Exists n. applys~ Nth_nth. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)