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