From 6b7c050f991cf7ed33bbceb0b3cdc530647eb261 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 19 Jul 2011 15:12:25 +0000
Subject: [PATCH] - drop_main: bug fix - pr_lift: closed!

---
 .../lib/lambda-delta/reduction/pr_lift.ma     | 57 +++++++++++++++++++
 .../lambda-delta/substitution/drop_main.ma    |  3 +-
 2 files changed, 59 insertions(+), 1 deletion(-)

diff --git a/matita/matita/lib/lambda-delta/reduction/pr_lift.ma b/matita/matita/lib/lambda-delta/reduction/pr_lift.ma
index 9718bf870..f5b4e0a37 100644
--- a/matita/matita/lib/lambda-delta/reduction/pr_lift.ma
+++ b/matita/matita/lib/lambda-delta/reduction/pr_lift.ma
@@ -67,3 +67,60 @@ lemma pr_lift: ∀L,T1,T2. L ⊢ T1 ⇒ T2 → ∀d,e,K. ↑[d,e] L ≡ K →
   @pr_tau /2 width=5/
 ]
 qed.
+
+lemma pr_inv_lift: ∀L,T1,T2. L ⊢ T1 ⇒ T2 →
+                   ∀d,e,K. ↑[d,e] K ≡ L → ∀U1. ↑[d,e] U1 ≡ T1 →
+                   ∃∃U2. ↑[d,e] U2 ≡ T2 & K ⊢ U1 ⇒ U2.
+#L #T1 #T2 #H elim H -H L T1 T2
+[ #L #k #d #e #K #_ #U1 #HU1
+  lapply (lift_inv_sort2 … HU1) -HU1 #H destruct -U1 /2/
+| #L #i #d #e #K #_ #U1 #HU1
+  lapply (lift_inv_lref2 … HU1) -HU1 * * #Hid #H destruct -U1 /3/
+| #L #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #K #HLK #X #HX
+  elim (lift_inv_bind2 … HX) -HX #V0 #T0 #HV01 #HT01 #HX destruct -X;
+  elim (IHV12 … HLK … HV01) -IHV12 #V3 #HV32 #HV03
+  elim (IHT12 … HT01) -IHT12 HT01 [2,3: -HV32 HV03 /3/] -HLK HV01 /3 width=5/
+| #L #I #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #K #HLK #X #HX
+  elim (lift_inv_flat2 … HX) -HX #V0 #T0 #HV01 #HT01 #HX destruct -X;
+  elim (IHV12 … HLK … HV01) -IHV12 HV01 #V3 #HV32 #HV03
+  elim (IHT12 … HLK … HT01) -IHT12 HT01 HLK /3 width=5/
+| #L #V1 #V2 #W1 #T1 #T2 #_ #_ #IHV12 #IHT12 #d #e #K #HLK #X #HX
+  elim (lift_inv_flat2 … HX) -HX #V0 #Y #HV01 #HY #HX destruct -X;
+  elim (lift_inv_bind2 … HY) -HY #W0 #T0 #HW01 #HT01 #HY destruct -Y;
+  elim (IHV12 … HLK … HV01) -IHV12 HV01 #V3 #HV32 #HV03
+  elim (IHT12 … HT01) -IHT12 HT01
+    [3: -HV32 HV03 @(drop_skip … HLK) /2/ |2: skip ] (**) (* /3 width=5/ is too slow *)
+    -HLK HW01
+  /3 width=5/
+| #L #K0 #V1 #V2 #V0 #i #HLK0 #HV12 #HV20 #IHV12 #d #e #K #HLK #X #HX
+  lapply (lift_inv_lref2 … HX) -HX * * #Hid #HX destruct -X;
+  [ -HV12;
+    elim (drop_conf_lt … HLK … HLK0 Hid) -HLK HLK0 L #L #V3 #HKL #HK0L #HV31
+    elim (IHV12 … HK0L … HV31) -IHV12 HK0L HV31 #V4 #HV42 #HV34
+    elim (lift_trans_le … HV42 … HV20 ?) -HV42 HV20 V2 // #V2 #HV42
+    >arith5 // -Hid #HV20  
+    @(ex2_1_intro … V2) /2 width=6/ (**) (* /3 width=8/ is slow *)
+  | -IHV12;
+    lapply (drop_conf_ge … HLK … HLK0 Hid) -HLK HLK0 L #HK
+    elim (lift_free … HV20 d (i - e + 1) ? ? ?) -HV20 /2/
+    >arith3 /2/ -Hid /3 width=8/ (**) (* just /3 width=8/ is a bit slow *)
+  ]
+| #L #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #d #e #K #HLK #X #HX
+  elim (lift_inv_flat2 … HX) -HX #V0 #Y #HV01 #HY #HX destruct -X;
+  elim (lift_inv_bind2 … HY) -HY #W0 #T0 #HW01 #HT01 #HY destruct -Y;
+  elim (IHV12 ? ? ? HLK ? HV01) -IHV12 HV01 #V3 #HV32 #HV03
+  elim (IHW12 ? ? ? HLK ? HW01) -IHW12 #W3 #HW32 #HW03
+  elim (IHT12 … HT01) -IHT12 HT01
+    [3: -HV2 HV32 HV03 HW32 HW03 @(drop_skip … HLK) /2/ |2: skip ] (**) (* /3/ is too slow *)
+    -HLK HW01 #T3 #HT32 #HT03
+  elim (lift_trans_le … HV32 … HV2 ?) -HV32 HV2 V2 // #V2 #HV32 #HV2
+  @(ex2_1_intro … (𝕓{Abbr}W3.𝕗{Appl}V2.T3)) /3/ (**) (* /4/ loops *)
+| #L #V #T #T1 #T2 #HT1 #_ #IHT12 #d #e #K #HLK #X #HX
+  elim (lift_inv_bind2 … HX) -HX #V0 #T0 #_ #HT0 #H destruct -X;
+  elim (lift_div_le … HT1 … HT0 ?) -HT1 HT0 T // #T #HT0 #HT1
+  elim (IHT12 … HLK … HT1) -IHT12 HLK HT1 /3 width=5/
+| #L #V #T1 #T2 #_ #IHT12 #d #e #K #HLK #X #HX
+  elim (lift_inv_flat2 … HX) -HX #V0 #T0 #_ #HT01 #H destruct -X;
+  elim (IHT12 … HLK … HT01) -IHT12 HLK HT01 /3/
+]
+qed.
diff --git a/matita/matita/lib/lambda-delta/substitution/drop_main.ma b/matita/matita/lib/lambda-delta/substitution/drop_main.ma
index f456b9e07..dc6f00d40 100644
--- a/matita/matita/lib/lambda-delta/substitution/drop_main.ma
+++ b/matita/matita/lib/lambda-delta/substitution/drop_main.ma
@@ -21,12 +21,13 @@ include "lambda-delta/substitution/drop_defs.ma".
 axiom drop_conf_ge: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
                     ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 + e1 ≤ e2 →
                     ↑[0, e2 - e1] L2 ≡ L1.
+      
 
 axiom drop_conf_lt: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
                     ∀e2,K2,I,V2. ↑[0, e2] K2. 𝕓{I} V2 ≡ L →
                     e2 < d1 → let d ≝ d1 - e2 - 1 in
                     ∃∃K1,V1. ↑[0, e2] K1. 𝕓{I} V1 ≡ L1 & 
-                             ↑[d, e1] K2 ≡ K1 & ↑[d,e1] V1 ≡ V2.
+                             ↑[d, e1] K1 ≡ K2 & ↑[d,e1] V1 ≡ V2.
 
 axiom drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
                      ∀e2,L2. ↑[0, e2] L2 ≡ L → e2 ≤ d1 →
-- 
2.39.2