- sone refactoring

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

diff --git a/matita/matita/lib/lambda-delta/substitution/drop_defs.ma b/matita/matita/lib/lambda-delta/substitution/drop_defs.ma
index 79af8f90da46c25c42e4d9c2f4ba3f0a757f3bea..1bf8e278d33ef4962ae8bfff4da40f094e74b7a8 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/drop_defs.ma
+++ b/matita/matita/lib/lambda-delta/substitution/drop_defs.ma
@@ -22,26 +22,56 @@ inductive drop: lenv → nat → nat → lenv → Prop ≝
              drop (L1. 𝕓{I} V1) (d + 1) e (L2. 𝕓{I} V2)
 .
 
-interpretation "dropping" 'RLift L2 d e L1 = (drop L1 d e L2).
+interpretation "dropping" 'RDrop L1 d e L2 = (drop L1 d e L2).
 
-(* the basic inversion lemmas ***********************************************)
+(* Basic properties *********************************************************) 
 
-lemma drop_inv_drop1_aux: ∀d,e,L2,L1. ↑[d, e] L2 ≡ L1 → 0 < e → d = 0 →
-                          ∀K,I,V. L1 = K. 𝕓{I} V → ↑[d, e - 1] L2 ≡ K.
-#d #e #L2 #L1 #H elim H -H d e L2 L1
-[ #L #H elim (lt_refl_false … H)
-| #L1 #L2 #I #V #e #HL12 #_ #_ #_ #K #J #W #H destruct -L1 I V //
-| #L1 #L2 #I #V1 #V2 #d #e #_ #_ #_ #_ #H elim (plus_S_eq_O_false … H)
+lemma drop_drop_lt: ∀L1,L2,I,V,e. 
+                    ↓[0, e - 1] L1 ≡ L2 → 0 < e → ↓[0, e] L1. 𝕓{I} V ≡ L2.
+#L1 #L2 #I #V #e #HL12 #He >(plus_minus_m_m e 1) /2/
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma 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 #e #_ #_ #_ #H
+  elim (plus_S_eq_O_false … H)
+| #L1 #L2 #I #V1 #V2 #d #e #_ #_ #_ #H
+  elim (plus_S_eq_O_false … H)
 ]
 qed.
 
-lemma drop_inv_drop1: ∀e,L2,K,I,V. ↑[0, e] L2 ≡ K. 𝕓{I} V → 0 < e →
-                                   ↑[0, e - 1] L2 ≡ K.
+lemma drop_inv_refl: ∀L1,L2. ↓[0, 0] L1 ≡ L2 → L1 = L2.
 /2 width=5/ qed.
 
-lemma drop_inv_skip2_aux: ∀d,e,L1,L2. ↑[d, e] L2 ≡ L1 → 0 < d →
+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).
+#d #e #L1 #L2 #H elim H -H d e L1 L2
+[ /3/
+| #L1 #L2 #I #V #e #HL12 #_ #_ #K #J #W #H destruct -L1 I V /3/
+| #L1 #L2 #I #V1 #V2 #d #e #_ #_ #_ #H elim (plus_S_eq_O_false … H)
+]
+qed.
+
+lemma drop_inv_O1: ∀e,K,I,V,L2. ↓[0, e] K. 𝕓{I} V ≡ L2 →
+                   (e = 0 ∧ L2 = K. 𝕓{I} V) ∨
+                   (0 < e ∧ ↓[0, e - 1] K ≡ L2).
+/2/ qed.
+
+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
+elim (drop_inv_O1 … H) -H * // #H destruct -e;
+elim (lt_refl_false … He)
+qed.
+
+lemma drop_inv_skip2_aux: ∀d,e,L1,L2. ↓[d, e] L1 ≡ L2 → 0 < d →
                           ∀I,K2,V2. L2 = K2. 𝕓{I} V2 →
-                          â\88\83â\88\83K1,V1. â\86\91[d - 1, e] K2 â\89¡ K1 &
+                          â\88\83â\88\83K1,V1. â\86\93[d - 1, e] K1 â\89¡ K2 &
                                    ↑[d - 1, e] V2 ≡ V1 & 
                                    L1 = K1. 𝕓{I} V1.
 #d #e #L1 #L2 #H elim H -H d e L1 L2
@@ -52,7 +82,7 @@ lemma drop_inv_skip2_aux: ∀d,e,L1,L2. ↑[d, e] L2 ≡ L1 → 0 < d →
 ]
 qed.
 
-lemma drop_inv_skip2: â\88\80d,e,I,L1,K2,V2. â\86\91[d, e] K2. ð\9d\95\93{I} V2 â\89¡ L1 → 0 < d →
-                      â\88\83â\88\83K1,V1. â\86\91[d - 1, e] K2 â\89¡ K1 & ↑[d - 1, e] V2 ≡ V1 &
+lemma drop_inv_skip2: â\88\80d,e,I,L1,K2,V2. â\86\93[d, e] L1 â\89¡ K2. ð\9d\95\93{I} V2 → 0 < d →
+                      â\88\83â\88\83K1,V1. â\86\93[d - 1, e] K1 â\89¡ K2 & ↑[d - 1, e] V2 ≡ V1 &
                                L1 = K1. 𝕓{I} V1.
 /2/ qed.