From 00cafb21b9177a6c48e51e97ba13aa1baad2c1b1 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Thu, 21 Jul 2011 13:40:24 +0000
Subject: [PATCH] one main propery of drop closed, one added

---
 matita/matita/lib/lambda-delta/ground.ma          |  3 +++
 .../lib/lambda-delta/substitution/drop_main.ma    | 15 ++++++++++++++-
 2 files changed, 17 insertions(+), 1 deletion(-)

diff --git a/matita/matita/lib/lambda-delta/ground.ma b/matita/matita/lib/lambda-delta/ground.ma
index b8c67bbcc..97c45196a 100644
--- a/matita/matita/lib/lambda-delta/ground.ma
+++ b/matita/matita/lib/lambda-delta/ground.ma
@@ -39,6 +39,9 @@ lemma le_plus_minus_comm: ∀n,m,p. p ≤ m → (m + n) - p = (m - p) + n.
 >(commutative_plus p) <plus_minus_m_m //
 qed.
 
+lemma le_plus_minus: ∀a,b,c. c ≤ b → a + b - c = a + (b - c).
+/2/ qed.
+
 lemma minus_le_minus_minus_comm: ∀m,p,n. 
                                  p ≤ m → m - p ≤ n → n + p - m = n - (m - p).
 #m elim m -m
diff --git a/matita/matita/lib/lambda-delta/substitution/drop_main.ma b/matita/matita/lib/lambda-delta/substitution/drop_main.ma
index 72d980e9b..4665b770c 100644
--- a/matita/matita/lib/lambda-delta/substitution/drop_main.ma
+++ b/matita/matita/lib/lambda-delta/substitution/drop_main.ma
@@ -73,5 +73,18 @@ lemma drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
 ]
 qed.
 
-axiom drop_trans_ge: ∀d1,e1,L1,L. ↑[d1, e1] L ≡ L1 →
+lemma drop_trans_ge: ∀d1,e1,L1,L. ↑[d1, e1] L ≡ L1 →
                      ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 ≤ e2 → ↑[0, e1 + e2] L2 ≡ L1.
+#d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
+[ //
+| /3/
+| #L1 #L2 #I #V1 #V2 #d #e #H_ #_ #IHL12 #e2 #L #H #Hde2
+  lapply (lt_to_le_to_lt 0 … Hde2) // #He2
+  lapply (lt_to_le_to_lt … (e + e2) He2 ?) // #Hee2
+  lapply (drop_inv_drop1 … H ?) -H // #HL2
+  @drop_drop_lt // >le_plus_minus // @IHL12 /2/ (**) (* explicit constructor *)
+]
+qed.
+
+axiom drop_div: ∀e1,L1. ∀L:lenv. ↑[0, e1] L ≡ L1 → ∀e2,L2. ↑[0, e2] L ≡ L2 →
+                ∃∃L0. ↑[0, e1] L2 ≡ L0 & ↑[e1, e2] L1 ≡ L0.
-- 
2.39.2