proposition: Lemma FS_red : forall ts t, FS t ts -> forall i, i < length ts -> red R (nth i (t::ts) default) (nth (S i) (t::ts) default).
proof: Proof. induction ts; simpl; intros. lia. destruct H. destruct i. hyp. ded (IHts _ H1 i (NatCompat.lt_S_n H0)). hyp. Qed.
imports: Coq(Euclid Wf_nat) CoLoR(LogicUtil Srs ListUtil EqUtil RelUtil ListDec NatUtil)