proposition: Lemma nth_app_l : forall n l1 l2, n < length l1 -> nth n (l1 ++ l2) = nth n l1.
proof: Proof. Proof using. introv N. applys nth_of_Nth. applys Nth_app_l. applys~ Nth_nth. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)