update in ground_2, static_2, basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpts_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_drops.ma
index a240f4a0eb8e2d9c75e2581d5aba03f5d0a19f9b..0754a138f205f24015467285521fb1db8b4db551 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_drops.ma
@@ -46,7 +46,7 @@ qed-.
 
 lemma cpts_delta (h) (n) (G):
       ∀K,V1,V2. ❪G,K❫ ⊢ V1 ⬆*[h,n] V2 →
-      ∀W2. ⇧*[1] V2 ≘ W2 → ❪G,K.ⓓV1❫ ⊢ #0 ⬆*[h,n] W2.
+      ∀W2. ⇧[1] V2 ≘ W2 → ❪G,K.ⓓV1❫ ⊢ #0 ⬆*[h,n] W2.
 #h #n #G #K #V1 #V2 #H @(cpts_ind_dx … H) -V2
 [ /3 width=3 by cpt_cpts, cpt_delta/
 | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2
@@ -57,7 +57,7 @@ qed.
 
 lemma cpts_ell (h) (n) (G):
       ∀K,V1,V2. ❪G,K❫ ⊢ V1 ⬆*[h,n] V2 →
-      ∀W2. ⇧*[1] V2 ≘ W2 → ❪G,K.ⓛV1❫ ⊢ #0 ⬆*[h,↑n] W2.
+      ∀W2. ⇧[1] V2 ≘ W2 → ❪G,K.ⓛV1❫ ⊢ #0 ⬆*[h,↑n] W2.
 #h #n #G #K #V1 #V2 #H @(cpts_ind_dx … H) -V2
 [ /3 width=3 by cpt_cpts, cpt_ell/
 | #n1 #n2 #V #V2 #_ #IH #HV2 #W2 #HVW2
@@ -68,7 +68,7 @@ qed.
 
 lemma cpts_lref (h) (n) (I) (G):
       ∀K,T,i. ❪G,K❫ ⊢ #i ⬆*[h,n] T →
-      ∀U. ⇧*[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬆*[h,n] U.
+      ∀U. ⇧[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬆*[h,n] U.
 #h #n #I #G #K #T #i #H @(cpts_ind_dx … H) -T
 [ /3 width=3 by cpt_cpts, cpt_lref/
 | #n1 #n2 #T #T2 #_ #IH #HT2 #U2 #HTU2
@@ -89,9 +89,9 @@ lemma cpts_cast_sn (h) (n) (G) (L):
 qed.
 
 lemma cpts_delta_drops (h) (n) (G):
-      ∀L,K,V,i. ⇩*[i] L ≘ K.ⓓV →
+      ∀L,K,V,i. ⇩[i] L ≘ K.ⓓV →
       ∀V2. ❪G,K❫ ⊢ V ⬆*[h,n] V2 →
-      ∀W2. ⇧*[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬆*[h,n] W2.
+      ∀W2. ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬆*[h,n] W2.
 #h #n #G #L #K #V #i #HLK #V2 #H @(cpts_ind_dx … H) -V2
 [ /3 width=6 by cpt_cpts, cpt_delta_drops/
 | #n1 #n2 #V1 #V2 #_ #IH #HV12 #W2 #HVW2
@@ -102,9 +102,9 @@ lemma cpts_delta_drops (h) (n) (G):
 qed.
 
 lemma cpts_ell_drops (h) (n) (G):
-      ∀L,K,W,i. ⇩*[i] L ≘ K.ⓛW →
+      ∀L,K,W,i. ⇩[i] L ≘ K.ⓛW →
       ∀W2. ❪G,K❫ ⊢ W ⬆*[h,n] W2 →
-      ∀V2. ⇧*[↑i] W2 ≘ V2 → ❪G,L❫ ⊢ #i ⬆*[h,↑n] V2.
+      ∀V2. ⇧[↑i] W2 ≘ V2 → ❪G,L❫ ⊢ #i ⬆*[h,↑n] V2.
 #h #n #G #L #K #W #i #HLK #W2 #H @(cpts_ind_dx … H) -W2
 [ /3 width=6 by cpt_cpts, cpt_ell_drops/
 | #n1 #n2 #W1 #W2 #_ #IH #HW12 #V2 #HWV2
@@ -119,8 +119,8 @@ qed.
 lemma cpts_inv_lref_sn_drops (h) (n) (G) (L) (i):
       ∀X2. ❪G,L❫ ⊢ #i ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #i & n = 0
-       | ∃∃K,V,V2. ⇩*[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ⬆*[h,n] V2 & ⇧*[↑i] V2 ≘ X2
-       | ∃∃m,K,V,V2. ⇩*[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ⬆*[h,m] V2 & ⇧*[↑i] V2 ≘ X2 & n = ↑m.
+       | ∃∃K,V,V2. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ⬆*[h,n] V2 & ⇧[↑i] V2 ≘ X2
+       | ∃∃m,K,V,V2. ⇩[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ⬆*[h,m] V2 & ⇧[↑i] V2 ≘ X2 & n = ↑m.
 #h #n #G #L #i #X2 #H @(cpts_ind_dx … H) -X2
 [ /3 width=1 by or3_intro0, conj/
 | #n1 #n2 #T #T2 #_ #IH #HT2 cases IH -IH *
@@ -145,7 +145,7 @@ qed-.
 lemma cpts_inv_delta_sn (h) (n) (G) (K) (V):
       ∀X2. ❪G,K.ⓓV❫ ⊢ #0 ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #0 & n = 0
-       | ∃∃V2. ❪G,K❫ ⊢ V ⬆*[h,n] V2 & ⇧*[1] V2 ≘ X2.
+       | ∃∃V2. ❪G,K❫ ⊢ V ⬆*[h,n] V2 & ⇧[1] V2 ≘ X2.
 #h #n #G #K #V #X2 #H
 elim (cpts_inv_lref_sn_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
@@ -160,7 +160,7 @@ qed-.
 lemma cpts_inv_ell_sn (h) (n) (G) (K) (V):
       ∀X2. ❪G,K.ⓛV❫ ⊢ #0 ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #0 & n = 0
-       | ∃∃m,V2. ❪G,K❫ ⊢ V ⬆*[h,m] V2 & ⇧*[1] V2 ≘ X2 & n = ↑m.
+       | ∃∃m,V2. ❪G,K❫ ⊢ V ⬆*[h,m] V2 & ⇧[1] V2 ≘ X2 & n = ↑m.
 #h #n #G #K #V #X2 #H
 elim (cpts_inv_lref_sn_drops … H) -H *
 [ /3 width=1 by or_introl, conj/
@@ -175,7 +175,7 @@ qed-.
 lemma cpts_inv_lref_sn (h) (n) (I) (G) (K) (i):
       ∀X2. ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #↑i & n = 0
-       | ∃∃T2. ❪G,K❫ ⊢ #i ⬆*[h,n] T2 & ⇧*[1] T2 ≘ X2.
+       | ∃∃T2. ❪G,K❫ ⊢ #i ⬆*[h,n] T2 & ⇧[1] T2 ≘ X2.
 #h #n #I #G #K #i #X2 #H
 elim (cpts_inv_lref_sn_drops … H) -H *
 [ /3 width=1 by or_introl, conj/