(*** minus_le *)
lemma nle_minus_sn_refl_sn (m) (n): m - n ≤ m.
-#m #n elim n -n //
+#m #n @(nat_ind_succ … n) -n //
#n #IH /2 width=3 by nle_trans/
qed.
(*** inv_eq_minus_O *)
lemma nle_eq_minus_O (m) (n): 𝟎 = m - n → m ≤ n.
-#m #n @(nat_ind_2 … m n) //
+#m #n @(nat_ind_succ_2 … m n) //
/3 width=1 by nle_succ_bi/
qed.
(*** monotonic_le_minus_l *)
lemma nle_minus_sn_bi (m) (n) (o): m ≤ n → m-o ≤ n-o.
-#m #n #o elim o -o //
+#m #n #o @(nat_ind_succ … o) -o //
#o #IH #Hmn /3 width=1 by nle_pred_bi/
qed.