From c88fe30a6900da730a684d7df6522407a388cd67 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 8 Jun 2014 18:34:23 +0000
Subject: [PATCH] now we use the version of lazy union for local environments
 in which the arguments have the same length. it should have better invariants

---
 .../contribs/lambdadelta/basic_2/multiple/llor.ma    |  6 +++---
 .../lambdadelta/basic_2/multiple/llor_etc.ma         | 12 +++++-------
 .../lambdadelta/basic_2/multiple/llor_ldrop.ma       |  4 ++--
 3 files changed, 10 insertions(+), 12 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor.ma
index fa3e511af..7832b4898 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor.ma
@@ -18,7 +18,7 @@ include "basic_2/multiple/frees.ma".
 (* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
 
 definition llor: ynat → relation4 term lenv lenv lenv ≝ λd,T,L2,L1,L.
-                 ∧∧ |L1| ≤ |L2| & |L1| = |L|
+                 ∧∧ |L1| = |L2| & |L1| = |L|
                   & (∀I1,I2,I,K1,K2,K,V1,V2,V,i.
                        ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → ⇩[i] L ≡ K.ⓑ{I}V → ∨∨
                        (∧∧ yinj i < d & I1 = I & V1 = V) |
@@ -33,8 +33,8 @@ interpretation
 (* Basic properties *********************************************************)
 
 (* Note: this can be proved by llor_skip *)
-lemma llor_atom: ∀L2,T,d. ⋆ ⩖[T, d] L2 ≡ ⋆.
-#L2 #T #d @and3_intro //
+lemma llor_atom: ∀T,d. ⋆ ⩖[T, d] ⋆ ≡ ⋆.
+#T #d @and3_intro //
 #I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
 elim (ldrop_inv_atom1 … HLK1) -HLK1 #H destruct
 qed.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_etc.ma
index 4ed8f333d..a1a80baa3 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_etc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_etc.ma
@@ -20,10 +20,10 @@ include "basic_2/multiple/llor_ldrop.ma".
 lemma lt_plus_SO_to_le: ∀x,y. x < y + 1 → x ≤ y.
 /2 width=1 by monotonic_pred/ qed-.
 
-(*
+
 lemma llor_tail_frees: ∀L1,L2,L,U,d. L1 ⩖[U, d] L2 ≡ L → d < yinj (|L1|) →
                        ∀I1,W1. ⓑ{I1}W1.L1 ⊢ |L1| ϵ 𝐅*[d]⦃U⦄ →
-                       ∀I2,W2. ⓑ{I1}W1.L1 ⩖[U, d] ⓑ{I2}W2.L2 ≡ ⓑ{I1}W2.L.
+                       ∀I2,W2. ⓑ{I1}W1.L1 ⩖[U, d] ⓑ{I2}W2.L2 ≡ ⓑ{I2}W2.L.
 #L1 #L2 #L #U #d * #HL12 #HL1 #IH #Hd #I1 #W1 #HU #I2 #W2
 @and3_intro [1,2: >ltail_length /2 width=1 by le_S_S/ ]
 #J1 #J2 #J #K1 #K2 #K #V1 #V2 #V #i #HLK1 #HLK2 #HLK
@@ -41,10 +41,8 @@ elim (le_to_or_lt_eq … H) -H #H
   | #HnU #HZ #HX
   | #Hdi #H2U #HZ #HX
   ]
-| -IH destruct
-  lapply (ldrop_O1_inv_append1_le … HLK1 … (⋆) ?) // -HLK1 normalize #H destruct
-  lapply (ldrop_O1_inv_append1_le … HLK2 … HL12)
+| -IH -HLK1 destruct
+  lapply (ldrop_O1_inv_append1_le … HLK2 … (⋆) ?) // -HLK2 normalize #H destruct
   lapply (ldrop_O1_inv_append1_le … HLK … (⋆) ?) // -HLK normalize #H destruct
-  @or3_intro2 @and4_intro /2 width=1 by ylt_fwd_le/
+  /4 width=1 by ylt_fwd_le, or3_intro2, and4_intro/
 ]
-*)
diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
index f8458d3c6..afc0924d9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
@@ -19,7 +19,7 @@ include "basic_2/multiple/llor.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma llor_skip: ∀L1,L2,U,d. |L1| ≤ |L2| → yinj (|L1|) ≤ d → L1 ⩖[U, d] L2 ≡ L1.
+lemma llor_skip: ∀L1,L2,U,d. |L1| = |L2| → yinj (|L1|) ≤ d → L1 ⩖[U, d] L2 ≡ L1.
 #L1 #L2 #U #d #HL12 #Hd @and3_intro // -HL12
 #I1 #I2 #I #K1 #K2 #K #W1 #W2 #W #i #HLK1 #_ #HLK -L2 -K2
 lapply (ldrop_mono … HLK … HLK1) -HLK #H destruct
@@ -27,4 +27,4 @@ lapply (ldrop_fwd_length_lt2 … HLK1) -K1
 /5 width=3 by ylt_yle_trans, ylt_inj, or3_intro0, and3_intro/
 qed.
 
-axiom llor_total: ∀L1,L2,T,d. |L1| ≤ |L2| → ∃L. L1 ⩖[T, d] L2 ≡ L.
+axiom llor_total: ∀L1,L2,T,d. |L1| = |L2| → ∃L. L1 ⩖[T, d] L2 ≡ L.
-- 
2.39.2