proposition: Lemma nth_mem : forall n l x, nth n l = x -> n < length l -> mem x l.
proof: Proof. Proof using. introv E N. forwards~ H: Nth_of_nth E. applys* Nth_mem H. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)