From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 5 Oct 2021 22:47:56 +0000 (+0200)
Subject: update in ground
X-Git-Tag: make_still_working~137
X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=commitdiff_plain;h=5d9f7ae4bad2b5926f615141c12942b9a8eb23fb

update in ground

+ one lemma was missing
---

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
index 5a6c4674b..61ab9b544 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground/generated/pull_2.ma".
 include "ground/arith/nat_le_minus.ma".
 include "ground/arith/nat_lt_pred.ma".
 
@@ -61,3 +62,21 @@ lemma nlt_des_minus_dx (o) (m) (n): m < n - o → o < n.
   /3 width=2 by nlt_inv_pred_dx/
 ]
 qed-.
+
+(* Advanced eliminators for nle with nlt and nminus *************************)
+
+(*** nat_elim_le_sn *)
+lemma nle_ind_sn (Q:relation …):
+      (∀m1,m2. (∀m. m < m2-m1 → Q (m2-m) m2) → m1 ≤ m2 → Q m1 m2) →
+      ∀n1,n2. n1 ≤ n2 → Q n1 n2.
+#Q #IH #n1 #n2 #Hn
+>(nminus_minus_dx_refl_sn … Hn) -Hn
+lapply (nle_minus_sn_refl_sn n2 n1)
+let d ≝ (n2-n1)
+@(nat_ind_lt … d) -d -n1 #d
+@pull_2 #Hd
+>(nminus_minus_dx_refl_sn … Hd) in ⊢ (%→?); -Hd
+let n1 ≝ (n2-d) #IHd
+@IH -IH [| // ] #m #Hn
+/4 width=3 by nlt_des_le, nlt_nle_trans/
+qed-.