update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma
index a8b160cd122254356839d9a299adaf50cd132833..59fe4d34e2f287c5141844c0aaa1cad3d8b631fc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma
@@ -22,7 +22,7 @@ include "basic_2/rt_transition/cpg.ma".
 (* T-BOUND CONTEXT-SENSITIVE PARALLEL T-TRANSITION FOR TERMS ****************)
 
 definition cpt (h) (G) (L) (n): relation2 term term ≝
-           λT1,T2. â\88\83â\88\83c. ð\9d\90\93â¦\83n,câ¦\84 & â¦\83G,Lâ¦\84 ⊢ T1 ⬈[eq …,c,h] T2.
+           λT1,T2. â\88\83â\88\83c. ð\9d\90\93â\9dªn,câ\9d« & â\9dªG,Lâ\9d« ⊢ T1 ⬈[eq …,c,h] T2.
 
 interpretation
   "t-bound context-sensitive parallel t-transition (term)"
@@ -31,53 +31,53 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma cpt_ess (h) (G) (L):
-      â\88\80s. â¦\83G,Lâ¦\84 ⊢ ⋆s ⬆[h,1] ⋆(⫯[h]s).
+      â\88\80s. â\9dªG,Lâ\9d« ⊢ ⋆s ⬆[h,1] ⋆(⫯[h]s).
 /2 width=3 by cpg_ess, ex2_intro/ qed.
 
 lemma cpt_delta (h) (n) (G) (K):
-      â\88\80V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬆[h,n] V2 →
-      â\88\80W2. â\87§*[1] V2 â\89\98 W2 â\86\92 â¦\83G,K.â\93\93V1â¦\84 ⊢ #0 ⬆[h,n] W2.
+      â\88\80V1,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.
 #h #n #G #K #V1 #V2 *
 /3 width=5 by cpg_delta, ex2_intro/
 qed.
 
 lemma cpt_ell (h) (n) (G) (K):
-      â\88\80V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬆[h,n] V2 →
-      â\88\80W2. â\87§*[1] V2 â\89\98 W2 â\86\92 â¦\83G,K.â\93\9bV1â¦\84 ⊢ #0 ⬆[h,↑n] W2.
+      â\88\80V1,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.
 #h #n #G #K #V1 #V2 *
 /3 width=5 by cpg_ell, ex2_intro, ist_succ/
 qed.
 
 lemma cpt_lref (h) (n) (G) (K):
-      â\88\80T,i. â¦\83G,Kâ¦\84 ⊢ #i ⬆[h,n] T → ∀U. ⇧*[1] T ≘ U →
-      â\88\80I. â¦\83G,K.â\93\98{I}â¦\84 ⊢ #↑i ⬆[h,n] U.
+      â\88\80T,i. â\9dªG,Kâ\9d« ⊢ #i ⬆[h,n] T → ∀U. ⇧*[1] T ≘ U →
+      â\88\80I. â\9dªG,K.â\93\98[I]â\9d« ⊢ #↑i ⬆[h,n] U.
 #h #n #G #K #T #i *
 /3 width=5 by cpg_lref, ex2_intro/
 qed.
 
 lemma cpt_bind (h) (n) (G) (L):
-      â\88\80V1,V2. â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\86[h,0] V2 â\86\92 â\88\80I,T1,T2. â¦\83G,L.â\93\91{I}V1â¦\84 ⊢ T1 ⬆[h,n] T2 →
-      â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T1 â¬\86[h,n] â\93\91{p,I}V2.T2.
+      â\88\80V1,V2. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\86[h,0] V2 â\86\92 â\88\80I,T1,T2. â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ⬆[h,n] T2 →
+      â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T1 â¬\86[h,n] â\93\91[p,I]V2.T2.
 #h #n #G #L #V1 #V2 * #cV #HcV #HV12 #I #T1 #T2 *
 /3 width=5 by cpg_bind, ist_max_O1, ex2_intro/
 qed.
 
 lemma cpt_appl (h) (n) (G) (L):
-      â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ⬆[h,0] V2 →
-      â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\86[h,n] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ ⓐV1.T1 ⬆[h,n] ⓐV2.T2.
+      â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬆[h,0] V2 →
+      â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\86[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ⬆[h,n] ⓐV2.T2.
 #h #n #G #L #V1 #V2 * #cV #HcV #HV12 #T1 #T2 *
 /3 width=5 by ist_max_O1, cpg_appl, ex2_intro/
 qed.
 
 lemma cpt_cast (h) (n) (G) (L):
-      â\88\80U1,U2. â¦\83G,Lâ¦\84 ⊢ U1 ⬆[h,n] U2 →
-      â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\86[h,n] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ ⓝU1.T1 ⬆[h,n] ⓝU2.T2.
+      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.
 #h #n #G #L #U1 #U2 * #cU #HcU #HU12 #T1 #T2 *
 /3 width=6 by cpg_cast, ex2_intro/
 qed.
 
 lemma cpt_ee (h) (n) (G) (L):
-      â\88\80U1,U2. â¦\83G,Lâ¦\84 â\8a¢ U1 â¬\86[h,n] U2 â\86\92 â\88\80T. â¦\83G,Lâ¦\84 ⊢ ⓝU1.T ⬆[h,↑n] U2.
+      â\88\80U1,U2. â\9dªG,Lâ\9d« â\8a¢ U1 â¬\86[h,n] U2 â\86\92 â\88\80T. â\9dªG,Lâ\9d« ⊢ ⓝU1.T ⬆[h,↑n] U2.
 #h #n #G #L #V1 #V2 *
 /3 width=3 by cpg_ee, ist_succ, ex2_intro/
 qed.
@@ -88,7 +88,7 @@ lemma cpt_refl (h) (G) (L): reflexive … (cpt h G L 0).
 (* Advanced properties ******************************************************)
 
 lemma cpt_sort (h) (G) (L):
-      â\88\80n. n â\89¤ 1 â\86\92 â\88\80s. â¦\83G,Lâ¦\84 ⊢ ⋆s ⬆[h,n] ⋆((next h)^n s).
+      â\88\80n. n â\89¤ 1 â\86\92 â\88\80s. â\9dªG,Lâ\9d« ⊢ ⋆s ⬆[h,n] ⋆((next h)^n s).
 #h #G #L * //
 #n #H #s <(le_n_O_to_eq n) /2 width=1 by le_S_S_to_le/
 qed.
@@ -96,12 +96,12 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 lemma cpt_inv_atom_sn (h) (n) (J) (G) (L):
-      â\88\80X2. â¦\83G,Lâ¦\84 â\8a¢ â\93ª{J} ⬆[h,n] X2 →
-      ∨∨ ∧∧ X2 = ⓪{J} & n = 0
+      â\88\80X2. â\9dªG,Lâ\9d« â\8a¢ â\93ª[J] ⬆[h,n] X2 →
+      ∨∨ ∧∧ X2 = ⓪[J] & n = 0
        | ∃∃s. X2 = ⋆(⫯[h]s) & J = Sort s & n =1
-       | â\88\83â\88\83K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬆[h,n] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓓV1 & J = LRef 0
-       | â\88\83â\88\83m,K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬆[h,m] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓛV1 & J = LRef 0 & n = ↑m
-       | â\88\83â\88\83I,K,T,i. â¦\83G,Kâ¦\84 â\8a¢ #i â¬\86[h,n] T & â\87§*[1] T â\89\98 X2 & L = K.â\93\98{I} & J = LRef (↑i).
+       | â\88\83â\88\83K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬆[h,n] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓓV1 & J = LRef 0
+       | â\88\83â\88\83m,K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬆[h,m] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓛV1 & J = LRef 0 & n = ↑m
+       | â\88\83â\88\83I,K,T,i. â\9dªG,Kâ\9d« â\8a¢ #i â¬\86[h,n] T & â\87§*[1] T â\89\98 X2 & L = K.â\93\98[I] & J = LRef (↑i).
 #h #n #J #G #L #X2 * #c #Hc #H
 elim (cpg_inv_atom1 … H) -H *
 [ #H1 #H2 destruct /3 width=1 by or5_intro0, conj/
@@ -117,7 +117,7 @@ elim (cpg_inv_atom1 … H) -H *
 qed-.
 
 lemma cpt_inv_sort_sn (h) (n) (G) (L) (s):
-      â\88\80X2. â¦\83G,Lâ¦\84 ⊢ ⋆s ⬆[h,n] X2 →
+      â\88\80X2. â\9dªG,Lâ\9d« ⊢ ⋆s ⬆[h,n] X2 →
       ∧∧ X2 = ⋆(((next h)^n) s) & n ≤ 1.
 #h #n #G #L #s #X2 * #c #Hc #H
 elim (cpg_inv_sort1 … H) -H * #H1 #H2 destruct
@@ -125,10 +125,10 @@ elim (cpg_inv_sort1 … H) -H * #H1 #H2 destruct
 qed-.
 
 lemma cpt_inv_zero_sn (h) (n) (G) (L):
-      â\88\80X2. â¦\83G,Lâ¦\84 ⊢ #0 ⬆[h,n] X2 →
+      â\88\80X2. â\9dªG,Lâ\9d« ⊢ #0 ⬆[h,n] X2 →
       ∨∨ ∧∧ X2 = #0 & n = 0
-       | â\88\83â\88\83K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬆[h,n] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓓV1
-       | â\88\83â\88\83m,K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬆[h,m] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓛV1 & n = ↑m.
+       | â\88\83â\88\83K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬆[h,n] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓓV1
+       | â\88\83â\88\83m,K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬆[h,m] V2 & ⇧*[1] V2 ≘ X2 & L = K.ⓛV1 & n = ↑m.
 #h #n #G #L #X2 * #c #Hc #H elim (cpg_inv_zero1 … H) -H *
 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or3_intro0, conj/
 | #cV #K #V1 #V2 #HV12 #HVT2 #H1 #H2 destruct
@@ -140,7 +140,7 @@ lemma cpt_inv_zero_sn (h) (n) (G) (L):
 qed-.
 
 lemma cpt_inv_zero_sn_unit (h) (n) (I) (K) (G):
-      â\88\80X2. â¦\83G,K.â\93¤{I}â¦\84 ⊢ #0 ⬆[h,n] X2 → ∧∧ X2 = #0 & n = 0.
+      â\88\80X2. â\9dªG,K.â\93¤[I]â\9d« ⊢ #0 ⬆[h,n] X2 → ∧∧ X2 = #0 & n = 0.
 #h #n #I #G #K #X2 #H
 elim (cpt_inv_zero_sn … H) -H *
 [ #H1 #H2 destruct /2 width=1 by conj/
@@ -150,9 +150,9 @@ elim (cpt_inv_zero_sn … H) -H *
 qed.
 
 lemma cpt_inv_lref_sn (h) (n) (G) (L) (i):
-      â\88\80X2. â¦\83G,Lâ¦\84 ⊢ #↑i ⬆[h,n] X2 →
+      â\88\80X2. â\9dªG,Lâ\9d« ⊢ #↑i ⬆[h,n] X2 →
       ∨∨ ∧∧ X2 = #(↑i) & n = 0
-       | â\88\83â\88\83I,K,T. â¦\83G,Kâ¦\84 â\8a¢ #i â¬\86[h,n] T & â\87§*[1] T â\89\98 X2 & L = K.â\93\98{I}.
+       | â\88\83â\88\83I,K,T. â\9dªG,Kâ\9d« â\8a¢ #i â¬\86[h,n] T & â\87§*[1] T â\89\98 X2 & L = K.â\93\98[I].
 #h #n #G #L #i #X2 * #c #Hc #H elim (cpg_inv_lref1 … H) -H *
 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or_introl, conj/
 | #I #K #V2 #HV2 #HVT2 #H destruct
@@ -161,7 +161,7 @@ lemma cpt_inv_lref_sn (h) (n) (G) (L) (i):
 qed-.
 
 lemma cpt_inv_lref_sn_ctop (n) (h) (G) (i):
-      â\88\80X2. â¦\83G,â\8b\86â¦\84 ⊢ #i ⬆[h,n] X2 → ∧∧ X2 = #i & n = 0.
+      â\88\80X2. â\9dªG,â\8b\86â\9d« ⊢ #i ⬆[h,n] X2 → ∧∧ X2 = #i & n = 0.
 #h #n #G * [| #i ] #X2 #H
 [ elim (cpt_inv_zero_sn … H) -H *
   [ #H1 #H2 destruct /2 width=1 by conj/
@@ -176,15 +176,15 @@ lemma cpt_inv_lref_sn_ctop (n) (h) (G) (i):
 qed.
 
 lemma cpt_inv_gref_sn (h) (n) (G) (L) (l):
-      â\88\80X2. â¦\83G,Lâ¦\84 ⊢ §l ⬆[h,n] X2 → ∧∧ X2 = §l & n = 0.
+      â\88\80X2. â\9dªG,Lâ\9d« ⊢ §l ⬆[h,n] X2 → ∧∧ X2 = §l & n = 0.
 #h #n #G #L #l #X2 * #c #Hc #H elim (cpg_inv_gref1 … H) -H
 #H1 #H2 destruct /2 width=1 by conj/
 qed-.
 
 lemma cpt_inv_bind_sn (h) (n) (p) (I) (G) (L) (V1) (T1):
-      â\88\80X2. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T1 ⬆[h,n] X2 →
-      â\88\83â\88\83V2,T2. â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\86[h,0] V2 & â¦\83G,L.â\93\91{I}V1â¦\84 ⊢ T1 ⬆[h,n] T2
-             & X2 = ⓑ{p,I}V2.T2.
+      â\88\80X2. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T1 ⬆[h,n] X2 →
+      â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\86[h,0] V2 & â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ⬆[h,n] T2
+             & X2 = ⓑ[p,I]V2.T2.
 #h #n #p #I #G #L #V1 #T1 #X2 * #c #Hc #H
 elim (cpg_inv_bind1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
@@ -197,8 +197,8 @@ elim (cpg_inv_bind1 … H) -H *
 qed-.
 
 lemma cpt_inv_appl_sn (h) (n) (G) (L) (V1) (T1):
-      â\88\80X2. â¦\83G,Lâ¦\84 ⊢ ⓐV1.T1 ⬆[h,n] X2 →
-      â\88\83â\88\83V2,T2. â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\86[h,0] V2 & â¦\83G,Lâ¦\84 ⊢ T1 ⬆[h,n] T2 & X2 = ⓐV2.T2.
+      â\88\80X2. â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ⬆[h,n] X2 →
+      â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\86[h,0] V2 & â\9dªG,Lâ\9d« ⊢ T1 ⬆[h,n] T2 & X2 = ⓐV2.T2.
 #h #n #G #L #V1 #T1 #X2 * #c #Hc #H elim (cpg_inv_appl1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
   elim (ist_inv_max … H2) -H2 #nV #nT #HcV #HcT #H destruct
@@ -212,9 +212,9 @@ lemma cpt_inv_appl_sn (h) (n) (G) (L) (V1) (T1):
 qed-.
 
 lemma cpt_inv_cast_sn (h) (n) (G) (L) (V1) (T1):
-      â\88\80X2. â¦\83G,Lâ¦\84 ⊢ ⓝV1.T1 ⬆[h,n] X2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\86[h,n] V2 & â¦\83G,Lâ¦\84 ⊢ T1 ⬆[h,n] T2 & X2 = ⓝV2.T2
-       | â\88\83â\88\83m. â¦\83G,Lâ¦\84 ⊢ V1 ⬆[h,m] X2 & n = ↑m.
+      â\88\80X2. â\9dªG,Lâ\9d« ⊢ ⓝV1.T1 ⬆[h,n] X2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\86[h,n] V2 & â\9dªG,Lâ\9d« ⊢ T1 ⬆[h,n] T2 & X2 = ⓝV2.T2
+       | â\88\83â\88\83m. â\9dªG,Lâ\9d« ⊢ V1 ⬆[h,m] X2 & n = ↑m.
 #h #n #G #L #V1 #T1 #X2 * #c #Hc #H elim (cpg_inv_cast1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #HcVT #H1 #H2 destruct
   elim (ist_inv_max … H2) -H2 #nV #nT #HcV #HcT #H destruct