proposition: Lemma mem_nth : forall l x, mem x l -> exists n, nth n l = x.
proof: Proof. Proof using. intros. forwards [n P]: mem_Nth H. exists n. apply~ nth_of_Nth. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)