proposition: Lemma nth_lt_length : forall x l, nth 0 (x::l) = x.
proof: Proof. Proof using. intros. apply nth_default_zero. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)