- predefined_virtuals: an addition

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma
index 7fbf16fbd8b339f5e2085881fe3d90b31776e01d..2608f02cec73d1540648cb663871b1176c47d36c 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma
@@ -14,87 +14,87 @@
 
 include "basic_2/unfold/tpss.ma".
 
-(* INVERSE TERM RELOCATION  *************************************************)
+(* INVERSE BASIC TERM RELOCATION  *******************************************)
 
 definition delift: nat → nat → lenv → relation term ≝
-                   λd,e,L,T1,T2. ∃∃T. L ⊢ T1 [d, e] ▶* T & ⇧[d, e] T2 ≡ T.
+                   λd,e,L,T1,T2. ∃∃T. L ⊢ T1 ▶* [d, e] T & ⇧[d, e] T2 ≡ T.
 
-interpretation "inverse relocation (term)"
+interpretation "inverse basic relocation (term)"
    'TSubst L T1 d e T2 = (delift d e L T1 T2).
 
 (* Basic properties *********************************************************)
 
 lemma lift_delift: ∀T1,T2,d,e. ⇧[d, e] T1 ≡ T2 →
-                   ∀L. L ⊢ T2 [d, e] ≡ T1.
+                   ∀L. L ⊢ T2 ▼*[d, e] ≡ T1.
 /2 width=3/ qed.
 
-lemma delift_refl_O2: ∀L,T,d. L ⊢ T [d, 0] ≡ T.
+lemma delift_refl_O2: ∀L,T,d. L ⊢ T ▼*[d, 0] ≡ T.
 /2 width=3/ qed.
 
-lemma delift_lsubs_conf: ∀L1,T1,T2,d,e. L1 ⊢ T1 [d, e] ≡ T2 →
-                         ∀L2. L1 [d, e] ≼ L2 → L2 ⊢ T1 [d, e] ≡ T2.
+lemma delift_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▼*[d, e] ≡ T2 →
+                          ∀L2. L2 ≼ [d, e] L1 → L2 ⊢ T1 ▼*[d, e] ≡ T2.
 #L1 #T1 #T2 #d #e * /3 width=3/
 qed.
 
-lemma delift_sort: ∀L,d,e,k. L ⊢ ⋆k [d, e] ≡ ⋆k.
+lemma delift_sort: ∀L,d,e,k. L ⊢ ⋆k ▼*[d, e] ≡ ⋆k.
 /2 width=3/ qed.
 
-lemma delift_lref_lt: ∀L,d,e,i. i < d → L ⊢ #i [d, e] ≡ #i.
+lemma delift_lref_lt: ∀L,d,e,i. i < d → L ⊢ #i ▼*[d, e] ≡ #i.
 /3 width=3/ qed.
 
-lemma delift_lref_ge: ∀L,d,e,i. d + e ≤ i → L ⊢ #i [d, e] ≡ #(i - e).
+lemma delift_lref_ge: ∀L,d,e,i. d + e ≤ i → L ⊢ #i ▼*[d, e] ≡ #(i - e).
 /3 width=3/ qed.
 
-lemma delift_gref: ∀L,d,e,p. L ⊢ §p [d, e] ≡ §p.
+lemma delift_gref: ∀L,d,e,p. L ⊢ §p ▼*[d, e] ≡ §p.
 /2 width=3/ qed.
 
 lemma delift_bind: ∀I,L,V1,V2,T1,T2,d,e.
-                   L ⊢ V1 [d, e] ≡ V2 → L. ⓑ{I} V2 ⊢ T1 [d+1, e] ≡ T2 →
-                   L ⊢ ⓑ{I} V1. T1 [d, e] ≡ ⓑ{I} V2. T2.
+                   L ⊢ V1 ▼*[d, e] ≡ V2 → L. ⓑ{I} V2 ⊢ T1 ▼*[d+1, e] ≡ T2 →
+                   L ⊢ ⓑ{I} V1. T1 ▼*[d, e] ≡ ⓑ{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 #d #e * #V #HV1 #HV2 * #T #HT1 #HT2
-lapply (tpss_lsubs_conf … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
+lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
 qed.
 
 lemma delift_flat: ∀I,L,V1,V2,T1,T2,d,e.
-                   L ⊢ V1 [d, e] ≡ V2 → L ⊢ T1 [d, e] ≡ T2 →
-                   L ⊢ ⓕ{I} V1. T1 [d, e] ≡ ⓕ{I} V2. T2.
+                   L ⊢ V1 ▼*[d, e] ≡ V2 → L ⊢ T1 ▼*[d, e] ≡ T2 →
+                   L ⊢ ⓕ{I} V1. T1 ▼*[d, e] ≡ ⓕ{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 #d #e * #V #HV1 #HV2 * /3 width=5/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma delift_inv_sort1: ∀L,U2,d,e,k. L ⊢ ⋆k [d, e] ≡ U2 → U2 = ⋆k.
+lemma delift_inv_sort1: ∀L,U2,d,e,k. L ⊢ ⋆k ▼*[d, e] ≡ U2 → U2 = ⋆k.
 #L #U2 #d #e #k * #U #HU
 >(tpss_inv_sort1 … HU) -HU #HU2
 >(lift_inv_sort2 … HU2) -HU2 //
 qed-.
 
-lemma delift_inv_gref1: ∀L,U2,d,e,p. L ⊢ §p [d, e] ≡ U2 → U2 = §p.
+lemma delift_inv_gref1: ∀L,U2,d,e,p. L ⊢ §p ▼*[d, e] ≡ U2 → U2 = §p.
 #L #U #d #e #p * #U #HU
 >(tpss_inv_gref1 … HU) -HU #HU2
 >(lift_inv_gref2 … HU2) -HU2 //
 qed-.
 
-lemma delift_inv_bind1: ∀I,L,V1,T1,U2,d,e. L ⊢ ⓑ{I} V1. T1 [d, e] ≡ U2 →
-                        ∃∃V2,T2. L ⊢ V1 [d, e] ≡ V2 &
-                                 L. ⓑ{I} V2 ⊢ T1 [d+1, e] ≡ T2 &
+lemma delift_inv_bind1: ∀I,L,V1,T1,U2,d,e. L ⊢ ⓑ{I} V1. T1 ▼*[d, e] ≡ U2 →
+                        ∃∃V2,T2. L ⊢ V1 ▼*[d, e] ≡ V2 &
+                                 L. ⓑ{I} V2 ⊢ T1 ▼*[d+1, e] ≡ T2 &
                                  U2 = ⓑ{I} V2. T2.
 #I #L #V1 #T1 #U2 #d #e * #U #HU #HU2
 elim (tpss_inv_bind1 … HU) -HU #V #T #HV1 #HT1 #X destruct
 elim (lift_inv_bind2 … HU2) -HU2 #V2 #T2 #HV2 #HT2
-lapply (tpss_lsubs_conf … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
+lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
 qed-.
 
-lemma delift_inv_flat1: ∀I,L,V1,T1,U2,d,e. L ⊢ ⓕ{I} V1. T1 [d, e] ≡ U2 →
-                        ∃∃V2,T2. L ⊢ V1 [d, e] ≡ V2 &
-                                 L ⊢ T1 [d, e] ≡ T2 &
+lemma delift_inv_flat1: ∀I,L,V1,T1,U2,d,e. L ⊢ ⓕ{I} V1. T1 ▼*[d, e] ≡ U2 →
+                        ∃∃V2,T2. L ⊢ V1 ▼*[d, e] ≡ V2 &
+                                 L ⊢ T1 ▼*[d, e] ≡ T2 &
                                  U2 = ⓕ{I} V2. T2.
 #I #L #V1 #T1 #U2 #d #e * #U #HU #HU2
 elim (tpss_inv_flat1 … HU) -HU #V #T #HV1 #HT1 #X destruct
 elim (lift_inv_flat2 … HU2) -HU2 /3 width=5/
 qed-.
 
-lemma delift_inv_refl_O2: ∀L,T1,T2,d. L ⊢ T1 [d, 0] ≡ T2 → T1 = T2.
+lemma delift_inv_refl_O2: ∀L,T1,T2,d. L ⊢ T1 ▼*[d, 0] ≡ T2 → T1 = T2.
 #L #T1 #T2 #d * #T #HT1
 >(tpss_inv_refl_O2 … HT1) -HT1 #HT2
 >(lift_inv_refl_O2 … HT2) -HT2 //