proposition: Lemma RS'_Hsep : forall (i j : nat) (Hi : S i <= m), j <= pred (sep__part_fun (S i) Hi) -> j <= n.
proof: Proof. intros. apply Nat.le_trans with (sep__part_fun (S i) Hi). 2: apply sep__part_fun_bnd. rewrite <- (Nat.lt_succ_pred (sep__part_fun i (Nat.lt_le_incl _ _ Hi)) (sep__part_fun (S i) Hi) ) . apply le_S; assumption. apply sep__part_fun_mon; apply Nat.lt_succ_diag_r. Qed.
imports: CoRN.ftc.COrdLemmas CoRN.ftc.Partitions Coq(Lia)