confluence of parallel substitution (tps) started ...

[helm.git] / matita / matita / lib / lambda-delta / substitution / drop_drop.ma

diff --git a/matita/matita/lib/lambda-delta/substitution/drop_drop.ma b/matita/matita/lib/lambda-delta/substitution/drop_drop.ma
index 135db64ca1852455154ec40628019c2a281bc7a3..812fb7e06bf1c449d1b2a2a339c59847d4cb6966 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/drop_drop.ma
+++ b/matita/matita/lib/lambda-delta/substitution/drop_drop.ma
@@ -12,15 +12,33 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "lambda-delta/substitution/lift_lift.ma".
 include "lambda-delta/substitution/drop.ma".
 
 (* DROPPING *****************************************************************)
 
 (* Main properties **********************************************************)
 
-lemma drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
-                    ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
-                    ↓[0, e2 - e1] L1 ≡ L2.
+theorem drop_mono: ∀d,e,L,L1. ↓[d, e] L ≡ L1 →
+                   ∀L2. ↓[d, e] L ≡ L2 → L1 = L2.
+#d #e #L #L1 #H elim H -H d e L L1
+[ #d #e #L2 #H
+  >(drop_inv_sort1 … H) -H L2 //
+| #K1 #K2 #I #V #HK12 #_ #L2 #HL12
+   <(drop_inv_refl … HK12) -HK12 K2
+   <(drop_inv_refl … HL12) -HL12 L2 //
+| #L #K #I #V #e #_ #IHLK #L2 #H
+  lapply (drop_inv_drop1 … H ?) -H /2/
+| #L #K1 #I #T #V1 #d #e #_ #HVT1 #IHLK1 #X #H
+  elim (drop_inv_skip1 … H ?) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct -X
+  >(lift_inj … HVT1 … HVT2) -HVT1 HVT2
+  >(IHLK1 … HLK2) -IHLK1 HLK2 // 
+]
+qed.
+
+theorem drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
+                      ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
+                      ↓[0, e2 - e1] L1 ≡ L2.
 #d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
 [ #d #e #e2 #L2 #H
   >(drop_inv_sort1 … H) -H L2 //
@@ -32,16 +50,16 @@ lemma drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
 | #L #K #I #V1 #V2 #d #e #_ #_ #IHLK #e2 #L2 #H #Hdee2
   lapply (transitive_le 1 … Hdee2) // #He2
   lapply (drop_inv_drop1 … H ?) -H // -He2 #HL2
-  lapply (transitive_le (1+e) … Hdee2) // #Hee2
+  lapply (transitive_le (1 + e) … Hdee2) // #Hee2
   @drop_drop_lt >minus_minus_comm /3/ (**) (* explicit constructor *)
 ]
 qed.
 
-lemma drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
-                    ∀e2,K2,I,V2. ↓[0, e2] L ≡ K2. 𝕓{I} V2 →
-                    e2 < d1 → let d ≝ d1 - e2 - 1 in
-                    ∃∃K1,V1. ↓[0, e2] L1 ≡ K1. 𝕓{I} V1 &
-                             ↓[d, e1] K2 ≡ K1 & ↑[d, e1] V1 ≡ V2.
+theorem drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
+                      ∀e2,K2,I,V2. ↓[0, e2] L ≡ K2. 𝕓{I} V2 →
+                      e2 < d1 → let d ≝ d1 - e2 - 1 in
+                      ∃∃K1,V1. ↓[0, e2] L1 ≡ K1. 𝕓{I} V1 &
+                               ↓[d, e1] K2 ≡ K1 & ↑[d, e1] V1 ≡ V2.
 #d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
 [ #d #e #e2 #K2 #I #V2 #H
   lapply (drop_inv_sort1 … H) -H #H destruct
@@ -58,9 +76,9 @@ lemma drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
 ]
 qed.
 
-lemma drop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
-                     ∀e2,L2. ↓[0, e2] L ≡ L2 → e2 ≤ d1 →
-                     ∃∃L0. ↓[0, e2] L1 ≡ L0 & ↓[d1 - e2, e1] L0 ≡ L2.
+theorem drop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
+                       ∀e2,L2. ↓[0, e2] L ≡ L2 → e2 ≤ d1 →
+                       ∃∃L0. ↓[0, e2] L1 ≡ L0 & ↓[d1 - e2, e1] L0 ≡ L2.
 #d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
 [ #d #e #e2 #L2 #H
   >(drop_inv_sort1 … H) -H L2 /2/
@@ -81,8 +99,8 @@ lemma drop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
 ]
 qed.
 
-lemma drop_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
-                     ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 ≤ e2 → ↓[0, e1 + e2] L1 ≡ L2.
+theorem drop_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
+                       ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 ≤ e2 → ↓[0, e1 + e2] L1 ≡ L2.
 #d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
 [ #d #e #e2 #L2 #H
   >(drop_inv_sort1 … H) -H L2 //
@@ -97,9 +115,9 @@ lemma drop_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
 ]
 qed.
 
-lemma drop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L.
-                          ↓[d1, e1] L1 ≡ L → ↓[0, e2] L ≡ L2 → d1 ≤ e2 →
-                          ↓[0, e2 + e1] L1 ≡ L2.
+theorem drop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L.
+                            ↓[d1, e1] L1 ≡ L → ↓[0, e2] L ≡ L2 → d1 ≤ e2 →
+                            ↓[0, e2 + e1] L1 ≡ L2.
 #e1 #e1 #e2 >commutative_plus /2 width=5/
 qed.