proposition: Lemma FS_red' : forall i, i < k - 1 -> red R (nth i) (nth (S i)).
proof: Proof. intros. unfold nth. change (red R (List.nth (S i) (t :: us) default) (List.nth (S (S i)) (t :: us) default)). apply FS_red. eapply rewrites_correct. apply h1. unfold k in *. lia. Qed.
imports: Coq(Euclid Wf_nat) CoLoR(LogicUtil Srs ListUtil EqUtil RelUtil ListDec NatUtil)