update in ground static_2 basic_2 apps_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 0754a138f205f24015467285521fb1db8b4db551..846d5eb51d2ef2947901691b1a54e62299014982 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
@@ -45,8 +45,8 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma cpts_delta (h) (n) (G):
-      â\88\80K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬆*[h,n] V2 →
-      â\88\80W2. â\87§[1] V2 â\89\98 W2 â\86\92 â\9dªG,K.â\93\93V1â\9d« ⊢ #0 ⬆*[h,n] W2.
+      â\88\80K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ⬆*[h,n] V2 →
+      â\88\80W2. â\87§[1] V2 â\89\98 W2 â\86\92 â\9d¨G,K.â\93\93V1â\9d© ⊢ #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
@@ -56,8 +56,8 @@ lemma cpts_delta (h) (n) (G):
 qed.
 
 lemma cpts_ell (h) (n) (G):
-      â\88\80K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬆*[h,n] V2 →
-      â\88\80W2. â\87§[1] V2 â\89\98 W2 â\86\92 â\9dªG,K.â\93\9bV1â\9d« ⊢ #0 ⬆*[h,↑n] W2.
+      â\88\80K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ⬆*[h,n] V2 →
+      â\88\80W2. â\87§[1] V2 â\89\98 W2 â\86\92 â\9d¨G,K.â\93\9bV1â\9d© ⊢ #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
@@ -67,8 +67,8 @@ lemma cpts_ell (h) (n) (G):
 qed.
 
 lemma cpts_lref (h) (n) (I) (G):
-      â\88\80K,T,i. â\9dªG,Kâ\9d« ⊢ #i ⬆*[h,n] T →
-      â\88\80U. â\87§[1] T â\89\98 U â\86\92 â\9dªG,K.â\93\98[I]â\9d« ⊢ #↑i ⬆*[h,n] U.
+      â\88\80K,T,i. â\9d¨G,Kâ\9d© ⊢ #i ⬆*[h,n] T →
+      â\88\80U. â\87§[1] T â\89\98 U â\86\92 â\9d¨G,K.â\93\98[I]â\9d© ⊢ #↑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
@@ -78,8 +78,8 @@ lemma cpts_lref (h) (n) (I) (G):
 qed.
 
 lemma cpts_cast_sn (h) (n) (G) (L):
-      â\88\80U1,U2. â\9dªG,Lâ\9d« ⊢ U1 ⬆*[h,n] U2 →
-      â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\86[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ⬆*[h,n] ⓝU2.T2.
+      â\88\80U1,U2. â\9d¨G,Lâ\9d© ⊢ U1 ⬆*[h,n] U2 →
+      â\88\80T1,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\86[h,n] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ ⓝU1.T1 ⬆*[h,n] ⓝU2.T2.
 #h #n #G #L #U1 #U2 #H @(cpts_ind_sn … H) -U1 -n
 [ /3 width=3 by cpt_cpts, cpt_cast/
 | #n1 #n2 #U1 #U #HU1 #_ #IH #T1 #T2 #H
@@ -90,8 +90,8 @@ qed.
 
 lemma cpts_delta_drops (h) (n) (G):
       ∀L,K,V,i. ⇩[i] L ≘ K.ⓓV →
-      â\88\80V2. â\9dªG,Kâ\9d« ⊢ V ⬆*[h,n] V2 →
-      â\88\80W2. â\87§[â\86\91i] V2 â\89\98 W2 â\86\92 â\9dªG,Lâ\9d« ⊢ #i ⬆*[h,n] W2.
+      â\88\80V2. â\9d¨G,Kâ\9d© ⊢ V ⬆*[h,n] V2 →
+      â\88\80W2. â\87§[â\86\91i] V2 â\89\98 W2 â\86\92 â\9d¨G,Lâ\9d© ⊢ #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
@@ -103,8 +103,8 @@ qed.
 
 lemma cpts_ell_drops (h) (n) (G):
       ∀L,K,W,i. ⇩[i] L ≘ K.ⓛW →
-      â\88\80W2. â\9dªG,Kâ\9d« ⊢ W ⬆*[h,n] W2 →
-      â\88\80V2. â\87§[â\86\91i] W2 â\89\98 V2 â\86\92 â\9dªG,Lâ\9d« ⊢ #i ⬆*[h,↑n] V2.
+      â\88\80W2. â\9d¨G,Kâ\9d© ⊢ W ⬆*[h,n] W2 →
+      â\88\80V2. â\87§[â\86\91i] W2 â\89\98 V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ #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
@@ -117,10 +117,10 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma cpts_inv_lref_sn_drops (h) (n) (G) (L) (i):
-      â\88\80X2. â\9dªG,Lâ\9d« ⊢ #i ⬆*[h,n] X2 →
+      â\88\80X2. â\9d¨G,Lâ\9d© ⊢ #i ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #i & n = 0
-       | â\88\83â\88\83K,V,V2. â\87©[i] L â\89\98 K.â\93\93V & â\9dªG,Kâ\9d« ⊢ V ⬆*[h,n] V2 & ⇧[↑i] V2 ≘ X2
-       | â\88\83â\88\83m,K,V,V2. â\87©[i] L â\89\98 K.â\93\9bV & â\9dªG,Kâ\9d« ⊢ V ⬆*[h,m] V2 & ⇧[↑i] V2 ≘ X2 & n = ↑m.
+       | â\88\83â\88\83K,V,V2. â\87©[i] L â\89\98 K.â\93\93V & â\9d¨G,Kâ\9d© ⊢ V ⬆*[h,n] V2 & ⇧[↑i] V2 ≘ X2
+       | â\88\83â\88\83m,K,V,V2. â\87©[i] L â\89\98 K.â\93\9bV & â\9d¨G,Kâ\9d© ⊢ 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 *
@@ -143,9 +143,9 @@ lemma cpts_inv_lref_sn_drops (h) (n) (G) (L) (i):
 qed-.
 
 lemma cpts_inv_delta_sn (h) (n) (G) (K) (V):
-      â\88\80X2. â\9dªG,K.â\93\93Vâ\9d« ⊢ #0 ⬆*[h,n] X2 →
+      â\88\80X2. â\9d¨G,K.â\93\93Vâ\9d© ⊢ #0 ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #0 & n = 0
-       | â\88\83â\88\83V2. â\9dªG,Kâ\9d« ⊢ V ⬆*[h,n] V2 & ⇧[1] V2 ≘ X2.
+       | â\88\83â\88\83V2. â\9d¨G,Kâ\9d© ⊢ 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/
@@ -158,9 +158,9 @@ elim (cpts_inv_lref_sn_drops … H) -H *
 qed-.
 
 lemma cpts_inv_ell_sn (h) (n) (G) (K) (V):
-      â\88\80X2. â\9dªG,K.â\93\9bVâ\9d« ⊢ #0 ⬆*[h,n] X2 →
+      â\88\80X2. â\9d¨G,K.â\93\9bVâ\9d© ⊢ #0 ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #0 & n = 0
-       | â\88\83â\88\83m,V2. â\9dªG,Kâ\9d« ⊢ V ⬆*[h,m] V2 & ⇧[1] V2 ≘ X2 & n = ↑m.
+       | â\88\83â\88\83m,V2. â\9d¨G,Kâ\9d© ⊢ 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/
@@ -173,9 +173,9 @@ elim (cpts_inv_lref_sn_drops … H) -H *
 qed-.
 
 lemma cpts_inv_lref_sn (h) (n) (I) (G) (K) (i):
-      â\88\80X2. â\9dªG,K.â\93\98[I]â\9d« ⊢ #↑i ⬆*[h,n] X2 →
+      â\88\80X2. â\9d¨G,K.â\93\98[I]â\9d© ⊢ #↑i ⬆*[h,n] X2 →
       ∨∨ ∧∧ X2 = #↑i & n = 0
-       | â\88\83â\88\83T2. â\9dªG,Kâ\9d« ⊢ #i ⬆*[h,n] T2 & ⇧[1] T2 ≘ X2.
+       | â\88\83â\88\83T2. â\9d¨G,Kâ\9d© ⊢ #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/
@@ -193,8 +193,8 @@ elim (cpts_inv_lref_sn_drops … H) -H *
 qed-.
 
 lemma cpts_inv_succ_sn (h) (n) (G) (L):
-      â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬆*[h,↑n] T2 →
-      â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\86*[h,1] T & â\9dªG,Lâ\9d« ⊢ T ⬆*[h,n] T2.
+      â\88\80T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬆*[h,↑n] T2 →
+      â\88\83â\88\83T. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\86*[h,1] T & â\9d¨G,Lâ\9d© ⊢ T ⬆*[h,n] T2.
 #h #n #G #L #T1 #T2
 @(insert_eq_0 … (↑n)) #m #H
 @(cpts_ind_sn … H) -T1 -m