proposition: Lemma In_L_aux_elim x k (h : k<n) : In x (L_aux h) -> exists i, N_val x = k - i.
proof: Proof. intro xL. destruct (In_nth x xL) as [i [i1 i2]]. apply N_eq in i2. rewrite nth_L_aux in i2. ex i. hyp. rewrite length_L_aux in i1. lia. Qed.
imports: CoLoR(LogicUtil NatUtil ListUtil ListNodup FunUtil VecUtil)