- xoa: bug fix and improvement

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

diff --git a/matita/matita/lib/lambda-delta/substitution/lift_defs.ma b/matita/matita/lib/lambda-delta/substitution/lift_defs.ma
index 472aef80969853afe20f07a93ee6565a702082b1..ff25453395ec6821bc489362ddcdcdc42b7f433f 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/lift_defs.ma
+++ b/matita/matita/lib/lambda-delta/substitution/lift_defs.ma
@@ -27,7 +27,7 @@ inductive lift: term → nat → nat → term → Prop ≝
 
 interpretation "relocation" 'RLift T1 d e T2 = (lift T1 d e T2).
 
-(* The basic properties *****************************************************)
+(* Basic properties *********************************************************)
 
 lemma lift_lref_ge_minus: ∀d,e,i. d + e ≤ i → ↑[d, e] #(i - e) ≡ #i.
 #d #e #i #H >(plus_minus_m_m i e) in ⊢ (? ? ? ? %) /3/
@@ -41,7 +41,7 @@ lemma lift_refl: ∀T,d. ↑[d, 0] T ≡ T.
 ]
 qed.
 
-(* The basic inversion lemmas ***********************************************)
+(* Basic inversion lemmas ***************************************************)
 
 lemma lift_inv_refl_aux: ∀d,e,T1,T2. ↑[d, e] T1 ≡ T2 → e = 0 → T1 = T2.
 #d #e #T1 #T2 #H elim H -H d e T1 T2 /3/
@@ -51,10 +51,10 @@ lemma lift_inv_refl: ∀d,T1,T2. ↑[d, 0] T1 ≡ T2 → T1 = T2.
 /2/ qed.
 
 lemma lift_inv_sort1_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 → ∀k. T1 = ⋆k → T2 = ⋆k.
-#d #e #T1 #T2 #H elim H -H d e T1 T2 //
+#d #e #T1 #T2 * -d e T1 T2 //
 [ #i #d #e #_ #k #H destruct
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #k #H destruct
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #k #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
 ]
 qed.
 
@@ -63,12 +63,12 @@ lemma lift_inv_sort1: ∀d,e,T2,k. ↑[d,e] ⋆k ≡ T2 → T2 = ⋆k.
 
 lemma lift_inv_lref1_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 → ∀i. T1 = #i →
                           (i < d ∧ T2 = #i) ∨ (d ≤ i ∧ T2 = #(i + e)).
-#d #e #T1 #T2 #H elim H -H d e T1 T2
+#d #e #T1 #T2 * -d e T1 T2
 [ #k #d #e #i #H destruct
 | #j #d #e #Hj #i #Hi destruct /3/
 | #j #d #e #Hj #i #Hi destruct /3/
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #i #H destruct
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #i #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct
 ]
 qed.
 
@@ -92,12 +92,12 @@ lemma lift_inv_bind1_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
                           ∀I,V1,U1. T1 = 𝕓{I} V1.U1 →
                           ∃∃V2,U2. ↑[d,e] V1 ≡ V2 & ↑[d+1,e] U1 ≡ U2 &
                                    T2 = 𝕓{I} V2. U2.
-#d #e #T1 #T2 #H elim H -H d e T1 T2
+#d #e #T1 #T2 * -d e T1 T2
 [ #k #d #e #I #V1 #U1 #H destruct
 | #i #d #e #_ #I #V1 #U1 #H destruct
 | #i #d #e #_ #I #V1 #U1 #H destruct
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V1 #U1 #H destruct /2 width=5/
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V1 #U1 #H destruct
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V1 #U1 #H destruct /2 width=5/
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V1 #U1 #H destruct
 ]
 qed.
 
@@ -110,12 +110,12 @@ lemma lift_inv_flat1_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
                           ∀I,V1,U1. T1 = 𝕗{I} V1.U1 →
                           ∃∃V2,U2. ↑[d,e] V1 ≡ V2 & ↑[d,e] U1 ≡ U2 &
                                    T2 = 𝕗{I} V2. U2.
-#d #e #T1 #T2 #H elim H -H d e T1 T2
+#d #e #T1 #T2 * -d e T1 T2
 [ #k #d #e #I #V1 #U1 #H destruct
 | #i #d #e #_ #I #V1 #U1 #H destruct
 | #i #d #e #_ #I #V1 #U1 #H destruct
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V1 #U1 #H destruct
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V1 #U1 #H destruct /2 width=5/
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V1 #U1 #H destruct
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V1 #U1 #H destruct /2 width=5/
 ]
 qed.
 
@@ -125,10 +125,10 @@ lemma lift_inv_flat1: ∀d,e,T2,I,V1,U1. ↑[d,e] 𝕗{I} V1. U1 ≡ T2 →
 /2/ qed.
 
 lemma lift_inv_sort2_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 → ∀k. T2 = ⋆k → T1 = ⋆k.
-#d #e #T1 #T2 #H elim H -H d e T1 T2 //
+#d #e #T1 #T2 * -d e T1 T2 //
 [ #i #d #e #_ #k #H destruct
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #k #H destruct
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #k #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #k #H destruct
 ]
 qed.
 
@@ -137,12 +137,12 @@ lemma lift_inv_sort2: ∀d,e,T1,k. ↑[d,e] T1 ≡ ⋆k → T1 = ⋆k.
 
 lemma lift_inv_lref2_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 → ∀i. T2 = #i →
                           (i < d ∧ T1 = #i) ∨ (d + e ≤ i ∧ T1 = #(i - e)).
-#d #e #T1 #T2 #H elim H -H d e T1 T2
+#d #e #T1 #T2 * -d e T1 T2
 [ #k #d #e #i #H destruct
 | #j #d #e #Hj #i #Hi destruct /3/
 | #j #d #e #Hj #i #Hi destruct <minus_plus_m_m /4/
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #i #H destruct
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #_ #_ #i #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct
+| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #i #H destruct
 ]
 qed.
 
@@ -166,12 +166,12 @@ lemma lift_inv_bind2_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
                           ∀I,V2,U2. T2 = 𝕓{I} V2.U2 →
                           ∃∃V1,U1. ↑[d,e] V1 ≡ V2 & ↑[d+1,e] U1 ≡ U2 &
                                    T1 = 𝕓{I} V1. U1.
-#d #e #T1 #T2 #H elim H -H d e T1 T2
+#d #e #T1 #T2 * -d e T1 T2
 [ #k #d #e #I #V2 #U2 #H destruct
 | #i #d #e #_ #I #V2 #U2 #H destruct
 | #i #d #e #_ #I #V2 #U2 #H destruct
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V2 #U2 #H destruct /2 width=5/
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V2 #U2 #H destruct
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V2 #U2 #H destruct /2 width=5/
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V2 #U2 #H destruct
 ]
 qed.
 
@@ -184,12 +184,12 @@ lemma lift_inv_flat2_aux: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 →
                           ∀I,V2,U2. T2 = 𝕗{I} V2.U2 →
                           ∃∃V1,U1. ↑[d,e] V1 ≡ V2 & ↑[d,e] U1 ≡ U2 &
                                    T1 = 𝕗{I} V1. U1.
-#d #e #T1 #T2 #H elim H -H d e T1 T2
+#d #e #T1 #T2 * -d e T1 T2
 [ #k #d #e #I #V2 #U2 #H destruct
 | #i #d #e #_ #I #V2 #U2 #H destruct
 | #i #d #e #_ #I #V2 #U2 #H destruct
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V2 #U2 #H destruct
-| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #_ #_ #I #V2 #U2 #H destruct /2 width = 5/
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V2 #U2 #H destruct
+| #J #W1 #W2 #T1 #T2 #d #e #HW #HT #I #V2 #U2 #H destruct /2 width = 5/
 ]
 qed.