update in ground static_2 basic_2 apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpm_teqx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx.ma
index e37493a83b7045ea20bfb9ff41849ef2a4edaa67..cd0203c84a821688471de95ae1c10d7759423a41 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx.ma
@@ -24,7 +24,7 @@ include "basic_2/dynamic/cnv_fsb.ma".
 (* Inversion lemmas with restricted rt-transition for terms *****************)
 
 lemma cnv_cpr_teqx_fwd_refl (h) (a) (G) (L):
-      â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,0] T2 â\86\92 T1 â\89\85 T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ![h,a] → T1 = T2.
+      â\88\80T1,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡[h,0] T2 â\86\92 T1 â\89\85 T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ![h,a] → T1 = T2.
 #h #a #G #L #T1 #T2 #H @(cpr_ind … H) -G -L -T1 -T2
 [ //
 | #G #K #V1 #V2 #X2 #_ #_ #_ #H1 #_ -a -G -K -V1 -V2
@@ -55,9 +55,9 @@ lemma cnv_cpr_teqx_fwd_refl (h) (a) (G) (L):
 qed-.
 
 lemma cpm_teqx_inv_bind_sn (h) (a) (n) (p) (I) (G) (L):
-      â\88\80V,T1. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V.T1 ![h,a] →
-      â\88\80X. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V.T1 ➡[h,n] X → ⓑ[p,I]V.T1 ≅ X →
-      â\88\83â\88\83T2. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] & â\9dªG,L.â\93\91[I]Vâ\9d« â\8a¢ T1 ![h,a] & â\9dªG,L.â\93\91[I]Vâ\9d« ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓑ[p,I]V.T2.
+      â\88\80V,T1. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V.T1 ![h,a] →
+      â\88\80X. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V.T1 ➡[h,n] X → ⓑ[p,I]V.T1 ≅ X →
+      â\88\83â\88\83T2. â\9d¨G,Lâ\9d© â\8a¢ V ![h,a] & â\9d¨G,L.â\93\91[I]Vâ\9d© â\8a¢ T1 ![h,a] & â\9d¨G,L.â\93\91[I]Vâ\9d© ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓑ[p,I]V.T2.
 #h #a #n #p #I #G #L #V #T1 #H0 #X #H1 #H2
 elim (cpm_inv_bind1 … H1) -H1 *
 [ #XV #T2 #HXV #HT12 #H destruct
@@ -73,10 +73,10 @@ elim (cpm_inv_bind1 … H1) -H1 *
 qed-.
 
 lemma cpm_teqx_inv_appl_sn (h) (a) (n) (G) (L):
-      â\88\80V,T1. â\9dªG,Lâ\9d« ⊢ ⓐV.T1 ![h,a] →
-      â\88\80X. â\9dªG,Lâ\9d« ⊢ ⓐV.T1 ➡[h,n] X → ⓐV.T1 ≅ X →
-      â\88\83â\88\83m,q,W,U1,T2. ad a m & â\9dªG,Lâ\9d« â\8a¢ V ![h,a] & â\9dªG,Lâ\9d« â\8a¢ V â\9e¡*[h,1] W & â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,m] ⓛ[q]W.U1
-                   & â\9dªG,Lâ\9d«â\8a¢ T1 ![h,a] & â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓐV.T2.
+      â\88\80V,T1. â\9d¨G,Lâ\9d© ⊢ ⓐV.T1 ![h,a] →
+      â\88\80X. â\9d¨G,Lâ\9d© ⊢ ⓐV.T1 ➡[h,n] X → ⓐV.T1 ≅ X →
+      â\88\83â\88\83m,q,W,U1,T2. ad a m & â\9d¨G,Lâ\9d© â\8a¢ V ![h,a] & â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡*[h,1] W & â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,m] ⓛ[q]W.U1
+                   & â\9d¨G,Lâ\9d©â\8a¢ T1 ![h,a] & â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓐV.T2.
 #h #a #n #G #L #V #T1 #H0 #X #H1 #H2
 elim (cpm_inv_appl1 … H1) -H1 *
 [ #XV #T2 #HXV #HT12 #H destruct
@@ -92,11 +92,11 @@ elim (cpm_inv_appl1 … H1) -H1 *
 qed-.
 
 lemma cpm_teqx_inv_cast_sn (h) (a) (n) (G) (L):
-      â\88\80U1,T1. â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ![h,a] →
-      â\88\80X. â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ➡[h,n] X → ⓝU1.T1 ≅ X →
-      â\88\83â\88\83U0,U2,T2. â\9dªG,Lâ\9d« â\8a¢ U1 â\9e¡*[h,0] U0 & â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,1] U0
-                & â\9dªG,Lâ\9d« â\8a¢ U1 ![h,a] & â\9dªG,Lâ\9d« ⊢ U1 ➡[h,n] U2 & U1 ≅ U2
-                & â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] & â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓝU2.T2.
+      â\88\80U1,T1. â\9d¨G,Lâ\9d© ⊢ ⓝU1.T1 ![h,a] →
+      â\88\80X. â\9d¨G,Lâ\9d© ⊢ ⓝU1.T1 ➡[h,n] X → ⓝU1.T1 ≅ X →
+      â\88\83â\88\83U0,U2,T2. â\9d¨G,Lâ\9d© â\8a¢ U1 â\9e¡*[h,0] U0 & â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,1] U0
+                & â\9d¨G,Lâ\9d© â\8a¢ U1 ![h,a] & â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,n] U2 & U1 ≅ U2
+                & â\9d¨G,Lâ\9d© â\8a¢ T1 ![h,a] & â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓝU2.T2.
 #h #a #n #G #L #U1 #T1 #H0 #X #H1 #H2
 elim (cpm_inv_cast1 … H1) -H1 [ * || * ]
 [ #U2 #T2 #HU12 #HT12 #H destruct
@@ -115,9 +115,9 @@ elim (cpm_inv_cast1 … H1) -H1 [ * || * ]
 qed-.
 
 lemma cpm_teqx_inv_bind_dx (h) (a) (n) (p) (I) (G) (L):
-      â\88\80X. â\9dªG,Lâ\9d« ⊢ X ![h,a] →
-      â\88\80V,T2. â\9dªG,Lâ\9d« ⊢ X ➡[h,n] ⓑ[p,I]V.T2 → X ≅ ⓑ[p,I]V.T2 →
-      â\88\83â\88\83T1. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] & â\9dªG,L.â\93\91[I]Vâ\9d« â\8a¢ T1 ![h,a] & â\9dªG,L.â\93\91[I]Vâ\9d« ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓑ[p,I]V.T1.
+      â\88\80X. â\9d¨G,Lâ\9d© ⊢ X ![h,a] →
+      â\88\80V,T2. â\9d¨G,Lâ\9d© ⊢ X ➡[h,n] ⓑ[p,I]V.T2 → X ≅ ⓑ[p,I]V.T2 →
+      â\88\83â\88\83T1. â\9d¨G,Lâ\9d© â\8a¢ V ![h,a] & â\9d¨G,L.â\93\91[I]Vâ\9d© â\8a¢ T1 ![h,a] & â\9d¨G,L.â\93\91[I]Vâ\9d© ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓑ[p,I]V.T1.
 #h #a #n #p #I #G #L #X #H0 #V #T2 #H1 #H2
 elim (teqx_inv_pair2 … H2) #V0 #T1 #_ #_ #H destruct
 elim (cpm_teqx_inv_bind_sn … H0 … H1 H2) -H0 -H1 -H2 #T0 #HV #HT1 #H1T12 #H2T12 #H destruct
@@ -129,23 +129,23 @@ qed-.
 lemma cpm_teqx_ind (h) (a) (n) (G) (Q:relation3 …):
       (∀I,L. n = 0 → Q L (⓪[I]) (⓪[I])) →
       (∀L,s. n = 1 → Q L (⋆s) (⋆(⫯[h]s))) →
-      (â\88\80p,I,L,V,T1. â\9dªG,Lâ\9d«â\8a¢ V![h,a] â\86\92 â\9dªG,L.â\93\91[I]Vâ\9d«⊢T1![h,a] →
-        â\88\80T2. â\9dªG,L.â\93\91[I]Vâ\9d« ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
+      (â\88\80p,I,L,V,T1. â\9d¨G,Lâ\9d©â\8a¢ V![h,a] â\86\92 â\9d¨G,L.â\93\91[I]Vâ\9d©⊢T1![h,a] →
+        â\88\80T2. â\9d¨G,L.â\93\91[I]Vâ\9d© ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
         Q (L.ⓑ[I]V) T1 T2 → Q L (ⓑ[p,I]V.T1) (ⓑ[p,I]V.T2)
       ) →
       (∀m. ad a m →
-        â\88\80L,V. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] â\86\92 â\88\80W. â\9dªG,Lâ\9d« ⊢ V ➡*[h,1] W →
-        â\88\80p,T1,U1. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,m] â\93\9b[p]W.U1 â\86\92 â\9dªG,Lâ\9d«⊢ T1 ![h,a] →
-        â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
+        â\88\80L,V. â\9d¨G,Lâ\9d© â\8a¢ V ![h,a] â\86\92 â\88\80W. â\9d¨G,Lâ\9d© ⊢ V ➡*[h,1] W →
+        â\88\80p,T1,U1. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,m] â\93\9b[p]W.U1 â\86\92 â\9d¨G,Lâ\9d©⊢ T1 ![h,a] →
+        â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
         Q L T1 T2 → Q L (ⓐV.T1) (ⓐV.T2)
       ) →
-      (â\88\80L,U0,U1,T1. â\9dªG,Lâ\9d« â\8a¢ U1 â\9e¡*[h,0] U0 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,1] U0 →
-        â\88\80U2. â\9dªG,Lâ\9d« â\8a¢ U1 ![h,a] â\86\92 â\9dªG,Lâ\9d« ⊢ U1 ➡[h,n] U2 → U1 ≅ U2 →
-        â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
+      (â\88\80L,U0,U1,T1. â\9d¨G,Lâ\9d© â\8a¢ U1 â\9e¡*[h,0] U0 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,1] U0 →
+        â\88\80U2. â\9d¨G,Lâ\9d© â\8a¢ U1 ![h,a] â\86\92 â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,n] U2 → U1 ≅ U2 →
+        â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 ![h,a] â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
         Q L U1 U2 → Q L T1 T2 → Q L (ⓝU1.T1) (ⓝU2.T2)
       ) →
-      â\88\80L,T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
-      â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 → Q L T1 T2.
+      â\88\80L,T1. â\9d¨G,Lâ\9d© ⊢ T1 ![h,a] →
+      â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 → Q L T1 T2.
 #h #a #n #G #Q #IH1 #IH2 #IH3 #IH4 #IH5 #L #T1
 @(insert_eq_0 … G) #F
 @(fqup_wf_ind_eq (Ⓣ) … F L T1) -L -T1 -F
@@ -170,9 +170,9 @@ qed-.
 (* Advanced properties with restricted rt-transition for terms **************)
 
 lemma cpm_teqx_free (h) (a) (n) (G) (L):
-      â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
-      â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
-      â\88\80F,K. â\9dªF,Kâ\9d« ⊢ T1 ➡[h,n] T2.
+      â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T1 ![h,a] →
+      â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
+      â\88\80F,K. â\9d¨F,Kâ\9d© ⊢ T1 ➡[h,n] T2.
 #h #a #n #G #L #T1 #H0 #T2 #H1 #H2
 @(cpm_teqx_ind … H0 … H1 H2) -L -T1 -T2
 [ #I #L #H #F #K destruct //
@@ -189,9 +189,9 @@ qed-.
 (* Advanced inversion lemmas with restricted rt-transition for terms ********)
 
 lemma cpm_teqx_inv_bind_sn_void (h) (a) (n) (p) (I) (G) (L):
-      â\88\80V,T1. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V.T1 ![h,a] →
-      â\88\80X. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V.T1 ➡[h,n] X → ⓑ[p,I]V.T1 ≅ X →
-      â\88\83â\88\83T2. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] & â\9dªG,L.â\93\91[I]Vâ\9d« â\8a¢ T1 ![h,a] & â\9dªG,L.â\93§â\9d« ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓑ[p,I]V.T2.
+      â\88\80V,T1. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V.T1 ![h,a] →
+      â\88\80X. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V.T1 ➡[h,n] X → ⓑ[p,I]V.T1 ≅ X →
+      â\88\83â\88\83T2. â\9d¨G,Lâ\9d© â\8a¢ V ![h,a] & â\9d¨G,L.â\93\91[I]Vâ\9d© â\8a¢ T1 ![h,a] & â\9d¨G,L.â\93§â\9d© ⊢ T1 ➡[h,n] T2 & T1 ≅ T2 & X = ⓑ[p,I]V.T2.
 #h #a #n #p #I #G #L #V #T1 #H0 #X #H1 #H2
 elim (cpm_teqx_inv_bind_sn … H0 … H1 H2) -H0 -H1 -H2 #T2 #HV #HT1 #H1T12 #H2T12 #H
 /3 width=5 by ex5_intro, cpm_teqx_free/