(*** lt_plus_to_minus *)
lemma nlt_minus_sn (o) (m) (n): m ≤ n → n < o + m → n - m < o.
#o #m #n #Hmn #Ho
-lapply (nle_minus_sn … Ho) -Ho
+lapply (nle_minus_sn_sn … Ho) -Ho
<nminus_succ_sn //
qed.
(*** lt_plus_to_minus_r *)
lemma nlt_minus_dx (o) (m) (n): m + o < n → m < n - o.
-/2 width=1 by nle_minus_dx/ qed.
+/2 width=1 by nle_minus_dx_sn/ qed.
(*** lt_inv_plus_l *)
lemma nlt_minus_dx_full (o) (m) (n): m + o < n → ∧∧ o < n & m < n - o.
-/3 width=3 by nlt_minus_dx, le_nlt_trans, conj/ qed-.
+/3 width=3 by nlt_minus_dx, nle_nlt_trans, conj/ qed-.
(* Inversions with nminus and nplus *****************************************)
lemma nlt_inv_minus_dx (o) (m) (n): m < n - o → m + o < n.
#o #m #n #Ho
lapply (nle_inv_minus_dx ???? Ho) //
-/3 width=2 by nlt_fwd_minus_dx, nlt_des_le/
+/3 width=2 by nlt_des_minus_dx, nlt_des_le/
qed-.