proposition: Lemma sep__part_fun_bnd' : forall (i : nat) (H : i <= m), i < m -> sep__part_fun i H < n.
proof: Proof. intros. unfold sep__part_fun in |- *. elim (le_lt_eq_dec _ _ H); intro; simpl in |- *. elim (ProjT2 sep__part_app_n). intros. apply H2. generalize a0; clear a0. unfold m in |- *; elim (RS'_delta2_delta4 RS'_m1); intro; simpl in |- *. auto with arith. auto with arith. rewrite b0 in H0; elim (Nat.lt_irrefl _ H0). Qed.
imports: CoRN.ftc.COrdLemmas CoRN.ftc.Partitions Coq(Lia)