- we shared the atomic term constructions

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / substitution / drop.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop.ma
index f9219f27f928469650e625739312a180aeed4944..65aaf3d4ee477da17109e981de3dfdde8f9ab448 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop.ma
@@ -12,11 +12,12 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic-2/substitution/leq.ma".
+include "Basic-2/grammar/leq.ma".
 include "Basic-2/substitution/lift.ma".
 
 (* DROPPING *****************************************************************)
 
+(* Basic-1: includes: drop_skip_bind *)
 inductive drop: lenv → nat → nat → lenv → Prop ≝
 | drop_sort: ∀d,e. drop (⋆) d e (⋆)
 | drop_comp: ∀L1,L2,I,V. drop L1 0 0 L2 → drop (L1. 𝕓{I} V) 0 0 (L2. 𝕓{I} V)
@@ -30,7 +31,7 @@ interpretation "dropping" 'RDrop L1 d e L2 = (drop L1 d e L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma drop_inv_refl_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → d = 0 → e = 0 → L1 = L2.
+fact drop_inv_refl_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → d = 0 → e = 0 → L1 = L2.
 #d #e #L1 #L2 #H elim H -H d e L1 L2
 [ //
 | #L1 #L2 #I #V #_ #IHL12 #H1 #H2
@@ -42,11 +43,12 @@ lemma drop_inv_refl_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → d = 0 → e = 0 
 ]
 qed.
 
+(* Basic-1: was: drop_gen_refl *)
 lemma drop_inv_refl: ∀L1,L2. ↓[0, 0] L1 ≡ L2 → L1 = L2.
 /2 width=5/ qed.
 
-lemma drop_inv_sort1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → L1 = ⋆ →
-                          L2 = ⋆.
+fact drop_inv_sort1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → L1 = ⋆ →
+                         L2 = ⋆.
 #d #e #L1 #L2 * -d e L1 L2
 [ //
 | #L1 #L2 #I #V #_ #H destruct
@@ -55,13 +57,14 @@ lemma drop_inv_sort1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → L1 = ⋆ →
 ]
 qed.
 
+(* Basic-1: was: drop_gen_sort *)
 lemma drop_inv_sort1: ∀d,e,L2. ↓[d, e] ⋆ ≡ L2 → L2 = ⋆.
 /2 width=5/ qed.
 
-lemma drop_inv_O1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → d = 0 →
-                       ∀K,I,V. L1 = K. 𝕓{I} V → 
-                       (e = 0 ∧ L2 = K. 𝕓{I} V) ∨
-                       (0 < e ∧ ↓[d, e - 1] K ≡ L2).
+fact drop_inv_O1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → d = 0 →
+                      ∀K,I,V. L1 = K. 𝕓{I} V → 
+                      (e = 0 ∧ L2 = K. 𝕓{I} V) ∨
+                      (0 < e ∧ ↓[d, e - 1] K ≡ L2).
 #d #e #L1 #L2 * -d e L1 L2
 [ #d #e #_ #K #I #V #H destruct
 | #L1 #L2 #I #V #HL12 #H #K #J #W #HX destruct -L1 I V
@@ -76,6 +79,7 @@ lemma drop_inv_O1: ∀e,K,I,V,L2. ↓[0, e] K. 𝕓{I} V ≡ L2 →
                    (0 < e ∧ ↓[0, e - 1] K ≡ L2).
 /2/ qed.
 
+(* Basic-1: was: drop_gen_drop *)
 lemma drop_inv_drop1: ∀e,K,I,V,L2.
                       ↓[0, e] K. 𝕓{I} V ≡ L2 → 0 < e → ↓[0, e - 1] K ≡ L2.
 #e #K #I #V #L2 #H #He
@@ -83,11 +87,11 @@ elim (drop_inv_O1 … H) -H * // #H destruct -e;
 elim (lt_refl_false … He)
 qed.
 
-lemma drop_inv_skip1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
-                          ∀I,K1,V1. L1 = K1. 𝕓{I} V1 →
-                          ∃∃K2,V2. ↓[d - 1, e] K1 ≡ K2 &
-                                   ↑[d - 1, e] V2 ≡ V1 & 
-                                   L2 = K2. 𝕓{I} V2.
+fact drop_inv_skip1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
+                         ∀I,K1,V1. L1 = K1. 𝕓{I} V1 →
+                         ∃∃K2,V2. ↓[d - 1, e] K1 ≡ K2 &
+                                  ↑[d - 1, e] V2 ≡ V1 & 
+                                  L2 = K2. 𝕓{I} V2.
 #d #e #L1 #L2 * -d e L1 L2
 [ #d #e #_ #I #K #V #H destruct
 | #L1 #L2 #I #V #_ #H elim (lt_refl_false … H)
@@ -97,17 +101,18 @@ lemma drop_inv_skip1_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
 ]
 qed.
 
+(* Basic-1: was: drop_gen_skip_l *)
 lemma drop_inv_skip1: ∀d,e,I,K1,V1,L2. ↓[d, e] K1. 𝕓{I} V1 ≡ L2 → 0 < d →
                       ∃∃K2,V2. ↓[d - 1, e] K1 ≡ K2 &
                                ↑[d - 1, e] V2 ≡ V1 & 
                                L2 = K2. 𝕓{I} V2.
 /2/ qed.
 
-lemma drop_inv_skip2_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
-                          ∀I,K2,V2. L2 = K2. 𝕓{I} V2 →
-                          ∃∃K1,V1. ↓[d - 1, e] K1 ≡ K2 &
-                                   ↑[d - 1, e] V2 ≡ V1 & 
-                                   L1 = K1. 𝕓{I} V1.
+fact drop_inv_skip2_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
+                         ∀I,K2,V2. L2 = K2. 𝕓{I} V2 →
+                         ∃∃K1,V1. ↓[d - 1, e] K1 ≡ K2 &
+                                  ↑[d - 1, e] V2 ≡ V1 & 
+                                  L1 = K1. 𝕓{I} V1.
 #d #e #L1 #L2 * -d e L1 L2
 [ #d #e #_ #I #K #V #H destruct
 | #L1 #L2 #I #V #_ #H elim (lt_refl_false … H)
@@ -117,6 +122,7 @@ lemma drop_inv_skip2_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
 ]
 qed.
 
+(* Basic-1: was: drop_gen_skip_r *)
 lemma drop_inv_skip2: ∀d,e,I,L1,K2,V2. ↓[d, e] L1 ≡ K2. 𝕓{I} V2 → 0 < d →
                       ∃∃K1,V1. ↓[d - 1, e] K1 ≡ K2 & ↑[d - 1, e] V2 ≡ V1 &
                                L1 = K1. 𝕓{I} V1.
@@ -124,6 +130,7 @@ lemma drop_inv_skip2: ∀d,e,I,L1,K2,V2. ↓[d, e] L1 ≡ K2. 𝕓{I} V2 → 0 <
 
 (* Basic properties *********************************************************)
 
+(* Basic-1: was by definition: drop_refl *)
 lemma drop_refl: ∀L. ↓[0, 0] L ≡ L.
 #L elim L -L /2/
 qed.
@@ -141,7 +148,7 @@ lemma drop_leq_drop1: ∀L1,L2,d,e. L1 [d, e] ≈ L2 →
 #L1 #L2 #d #e #H elim H -H L1 L2 d e
 [ #d #e #I #K1 #V #i #H
   lapply (drop_inv_sort1 … H) -H #H destruct
-| #L1 #L2 #I1 #I2 #V1 #V2 #_ #_ #I #K1 #V #i #_ #_ #H
+| #L1 #L2 #I #K1 #V #i #_ #_ #H
   elim (lt_zero_false … H)
 | #L1 #L2 #I #V #e #HL12 #IHL12 #J #K1 #W #i #H #_ #Hie
   elim (drop_inv_O1 … H) -H * #Hi #HLK1
@@ -159,6 +166,7 @@ qed.
 
 (* Basic forvard lemmas *****************************************************)
 
+(* Basic-1: was: drop_S *)
 lemma drop_fwd_drop2: ∀L1,I2,K2,V2,e. ↓[O, e] L1 ≡ K2. 𝕓{I2} V2 →
                       ↓[O, e + 1] L1 ≡ K2.
 #L1 elim L1 -L1
@@ -194,3 +202,12 @@ lemma drop_fwd_O1_length: ∀L1,L2,e. ↓[0, e] L1 ≡ L2 → |L2| = |L1| - e.
   ]
 ]
 qed.
+
+(* Basic-1: removed theorems 18:
+            drop_skip_flat
+            cimp_flat_sx cimp_flat_dx cimp_bind cimp_getl_conf
+            drop_clear drop_clear_O drop_clear_S
+            clear_gen_sort clear_gen_bind clear_gen_flat clear_gen_flat_r
+            clear_gen_all clear_clear clear_mono clear_trans clear_ctail
+            clear_cle
+*)