+(*** minus_pred_pred *)
+lemma nminus_pred_bi (m) (n): 𝟎 < m → 𝟎 < n → n - m = ↓n - ↓m.
+#m #n #Hm #Hn
+>(nlt_des_gen … Hm) in ⊢ (??%?); -Hm
+>(nlt_des_gen … Hn) in ⊢ (??%?); -Hn
+//
+qed-.
+
+lemma nlt_des_minus_dx (o) (m) (n): m < n - o → o < n.
+#o @(nat_ind_succ … o) -o