proposition: Lemma Nth_of_nth_default : forall l d n x, nth_default d n l = x -> n < length l -> Nth n l x.
proof: Proof. Proof using. intros l. induction l; rew_list; introv E N. { false. math. } { destruct n; simpls. { subst*. } { constructors. applys* IHl. math. } } Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)