- predefined_virtuals: some additions

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / delift_lift.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_lift.ma
index 490c6ac5b1dcb0de7367792e32a1a20207c1f5c3..d8c74669767fd9bec09fc9a489e63dfa295acbec 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_lift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift_lift.ma
@@ -20,8 +20,8 @@ include "basic_2/unfold/delift.ma".
 (* Advanced properties ******************************************************)
 
 lemma delift_lref_be: ∀L,K,V1,V2,U2,i,d,e. d ≤ i → i < d + e →
-                      ⇩[0, i] L ≡ K. ⓓV1 → K ⊢ V1 [0, d + e - i - 1] ≡ V2 →
-                      ⇧[0, d] V2 ≡ U2 → L ⊢ #i [d, e] ≡ U2.
+                      ⇩[0, i] L ≡ K. ⓓV1 → K ⊢ V1 ▼*[0, d + e - i - 1] ≡ V2 →
+                      ⇧[0, d] V2 ≡ U2 → L ⊢ #i ▼*[d, e] ≡ U2.
 #L #K #V1 #V2 #U2 #i #d #e #Hdi #Hide #HLK * #V #HV1 #HV2 #HVU2
 elim (lift_total V 0 (i+1)) #U #HVU
 lapply (lift_trans_be … HV2 … HVU ? ?) -HV2 // >minus_plus <plus_minus_m_m /2 width=1/ #HV2U 
@@ -31,7 +31,7 @@ qed.
  
 (* Advanced inversion lemmas ************************************************)
 
-lemma delift_inv_lref1_lt: ∀L,U2,i,d,e. L ⊢ #i [d, e] ≡ U2 → i < d → U2 = #i.
+lemma delift_inv_lref1_lt: ∀L,U2,i,d,e. L ⊢ #i ▼*[d, e] ≡ U2 → i < d → U2 = #i.
 #L #U2 #i #d #e * #U #HU #HU2 #Hid
 elim (tpss_inv_lref1 … HU) -HU
 [ #H destruct >(lift_inv_lref2_lt … HU2) //
@@ -41,10 +41,10 @@ elim (tpss_inv_lref1 … HU) -HU
 ]
 qed-.
 
-lemma delift_inv_lref1_be: ∀L,U2,d,e,i. L ⊢ #i [d, e] ≡ U2 →
+lemma delift_inv_lref1_be: ∀L,U2,d,e,i. L ⊢ #i ▼*[d, e] ≡ U2 →
                            d ≤ i → i < d + e →
                            ∃∃K,V1,V2. ⇩[0, i] L ≡ K. ⓓV1 &
-                                      K ⊢ V1 [0, d + e - i - 1] ≡ V2 &
+                                      K ⊢ V1 ▼*[0, d + e - i - 1] ≡ V2 &
                                       ⇧[0, d] V2 ≡ U2.
 #L #U2 #d #e #i * #U #HU #HU2 #Hdi #Hide
 elim (tpss_inv_lref1 … HU) -HU
@@ -54,7 +54,7 @@ elim (tpss_inv_lref1 … HU) -HU
 ]
 qed-.
 
-lemma delift_inv_lref1_ge: ∀L,U2,i,d,e. L ⊢ #i [d, e] ≡ U2 →
+lemma delift_inv_lref1_ge: ∀L,U2,i,d,e. L ⊢ #i ▼*[d, e] ≡ U2 →
                            d + e ≤ i → U2 = #(i - e).
 #L #U2 #i #d #e * #U #HU #HU2 #Hdei
 elim (tpss_inv_lref1 … HU) -HU
@@ -65,11 +65,11 @@ elim (tpss_inv_lref1 … HU) -HU
 ]
 qed-.
 
-lemma delift_inv_lref1: ∀L,U2,i,d,e. L ⊢ #i [d, e] ≡ U2 →
+lemma delift_inv_lref1: ∀L,U2,i,d,e. L ⊢ #i ▼*[d, e] ≡ U2 →
                         ∨∨ (i < d ∧ U2 = #i) 
                         |  (∃∃K,V1,V2. d ≤ i & i < d + e &
                                        ⇩[0, i] L ≡ K. ⓓV1 &
-                                       K ⊢ V1 [0, d + e - i - 1] ≡ V2 &
+                                       K ⊢ V1 ▼*[0, d + e - i - 1] ≡ V2 &
                                        ⇧[0, d] V2 ≡ U2
                            )
                         |  (d + e ≤ i ∧ U2 = #(i - e)).
@@ -85,10 +85,10 @@ qed-.
 
 (* Properties on basic term relocation **************************************)
 
-lemma delift_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≡ T2 →
+lemma delift_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 ▼*[dt, et] ≡ T2 →
                       ∀L,U1,d,e. dt + et ≤ d → ⇩[d, e] L ≡ K →
                       ⇧[d, e] T1 ≡ U1 → ∀U2. ⇧[d - et, e] T2 ≡ U2 →
-                      L ⊢ U1 [dt, et] ≡ U2.
+                      L ⊢ U1 ▼*[dt, et] ≡ U2.
 #K #T1 #T2 #dt #et * #T #HT1 #HT2 #L #U1 #d #e #Hdetd #HLK #HTU1 #U2 #HTU2
 elim (lift_total T d e) #U #HTU
 lapply (tpss_lift_le … HT1 … HLK HTU1 … HTU) -T1 -HLK // #HU1
@@ -96,20 +96,20 @@ elim (lift_trans_ge … HT2 … HTU ?) -T // -Hdetd #T #HT2 #HTU
 >(lift_mono … HTU2 … HT2) -T2 /2 width=3/
 qed.
 
-lemma delift_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≡ T2 →
+lemma delift_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 ▼*[dt, et] ≡ T2 →
                       ∀L,U1,d,e. dt ≤ d → d ≤ dt + et →
                       ⇩[d, e] L ≡ K → ⇧[d, e] T1 ≡ U1 →
-                      L ⊢ U1 [dt, et + e] ≡ T2.
+                      L ⊢ U1 ▼*[dt, et + e] ≡ T2.
 #K #T1 #T2 #dt #et * #T #HT1 #HT2 #L #U1 #d #e #Hdtd #Hddet #HLK #HTU1
 elim (lift_total T d e) #U #HTU
 lapply (tpss_lift_be … HT1 … HLK HTU1 … HTU) -T1 -HLK // #HU1
 lapply (lift_trans_be … HT2 … HTU ? ?) -T // -Hdtd -Hddet /2 width=3/
 qed.
 
-lemma delift_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≡ T2 →
+lemma delift_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 ▼*[dt, et] ≡ T2 →
                       ∀L,U1,d,e. d ≤ dt → ⇩[d, e] L ≡ K →
                       ⇧[d, e] T1 ≡ U1 → ∀U2. ⇧[d, e] T2 ≡ U2 →
-                      L ⊢ U1 [dt + e, et] ≡ U2.
+                      L ⊢ U1 ▼*[dt + e, et] ≡ U2.
 #K #T1 #T2 #dt #et * #T #HT1 #HT2 #L #U1 #d #e #Hddt #HLK #HTU1 #U2 #HTU2
 elim (lift_total T d e) #U #HTU
 lapply (tpss_lift_ge … HT1 … HLK HTU1 … HTU) -T1 -HLK // #HU1
@@ -117,9 +117,9 @@ elim (lift_trans_le … HT2 … HTU ?) -T // -Hddt #T #HT2 #HTU
 >(lift_mono … HTU2 … HT2) -T2 /2 width=3/
 qed.
 
-lemma delift_lift_div_be: ∀L,T1,T,d,e,i. L ⊢ T1 [i, d + e - i] ≡ T →
+lemma delift_lift_div_be: ∀L,T1,T,d,e,i. L ⊢ T1 ▼*[i, d + e - i] ≡ T →
                           ∀T2. ⇧[d, i - d] T2 ≡ T → d ≤ i → i ≤ d + e →
-                          L ⊢ T1 [d, e] ≡ T2.
+                          L ⊢ T1 ▼*[d, e] ≡ T2.
 #L #T1 #T #d #e #i * #T0 #HT10 #HT0 #T2 #HT2 #Hdi #Hide
 lapply (tpss_weak … HT10 d e ? ?) -HT10 // [ >commutative_plus /2 width=1/ ] #HT10
 lapply (lift_trans_be … HT2 … HT0 ? ?) -T //