proposition: Lemma length_remove_nodup (x : A) : forall l, nodup l -> In x l -> length (remove eq_dec x l) = length l - 1.
proof: Proof. induction l; intros hl ha; simpl. refl. destruct (eq_dec a x). subst. rewrite remove_notin. lia. fo. simpl. rewrite IHl. destruct l. fo. simpl. lia. fo. fo. Qed.
imports: CoLoR(ListUtil NatUtil RelMidex LogicUtil)