From 41a54a797af98d2867d4bf979d424283fb44a1fc Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 4 Sep 2022 21:25:25 +0200
Subject: [PATCH] update in ground

+ some renaming and some refactoring
---
 .../lambdadelta/ground/arith/nat_le_pred.ma   | 33 +++++++++++--------
 .../ground/relocation/tr_uni_compose.ma       |  2 +-
 2 files changed, 21 insertions(+), 14 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
index b5347a806..1666a5548 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
@@ -17,13 +17,31 @@ include "ground/arith/nat_le.ma".
 
 (* ORDER FOR NON-NEGATIVE INTEGERS ******************************************)
 
-(* Destructions with npred **************************************************)
+(* Inversions with npred ****************************************************)
 
 lemma nle_inv_pred_sn (m) (n): ↓m ≤ n → m ≤ ↑n.
 #m #n @(nat_ind_succ … m) -m
 /2 width=1 by nle_succ_bi/
 qed-.
 
+(*** le_inv_S1 *)
+lemma nle_inv_succ_sn (m) (n):
+      ↑m ≤ n → ∧∧ m ≤ ↓n & n = ↑↓n.
+#m #n * -n
+[ /2 width=3 by nle_refl, conj/
+| #n #Hn /3 width=1 by nle_des_succ_sn, conj/
+]
+qed-.
+
+lemma nle_inv_succ_dx (m) (n):
+      m ≤ ↑n → ∨∨ 𝟎 = m | ∧∧ ↓m ≤ n & m = ↑↓m.
+#m #n @(nat_ind_succ … m) -m
+[ /2 width=1 by or_introl/
+| #m #_ #H0
+  /4 width=1 by nle_inv_succ_bi, or_intror, conj/
+]
+qed-.
+
 (* Constructions with npred *************************************************)
 
 lemma nle_succ_pred_dx_refl (m): m ≤ ↑↓m.
@@ -43,15 +61,4 @@ qed.
 lemma nle_pred_sn (m) (n): m ≤ ↑n → ↓m ≤ n.
 #m #n @(nat_ind_succ … m) -m //
 /2 width=1 by nle_pred_bi/
-qed-.
-
-(* Inversions with npred ****************************************************)
-
-(*** le_inv_S1 *)
-lemma nle_inv_succ_sn (m) (n):
-      ↑m ≤ n → ∧∧ m ≤ ↓n & n = ↑↓n.
-#m #n * -n
-[ /2 width=3 by nle_refl, conj/
-| #n #Hn /3 width=1 by nle_des_succ_sn, conj/
-]
-qed-.
+qed.
diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/tr_uni_compose.ma b/matita/matita/contribs/lambdadelta/ground/relocation/tr_uni_compose.ma
index 92315b6a6..2343c74ac 100644
--- a/matita/matita/contribs/lambdadelta/ground/relocation/tr_uni_compose.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/tr_uni_compose.ma
@@ -50,7 +50,7 @@ qed.
 
 (* Main constructions with tr_compose and tr_tls ****************************)
 
-theorem tr_compose_uni_dx (f) (p):
+theorem tr_compose_uni_dx_pap (f) (p):
         (𝐮❨f＠⧣❨p❩❩∘⇂*[p]f) ≗ f∘𝐮❨p❩.
 #f #p
 @nstream_eq_inv_ext #q
-- 
2.39.2