update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 1cc63fbae6151485247840bbf8075b679f9e0859..4a5e09ff81dce6f99cd0ff0fdcdc614a442c7a49 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¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[h] T2 â\86\92 T1 â\89\9b T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ![h,a] → T1 = T2.
+      â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T2 â\86\92 T1 â\89\9b T2 â\86\92 â\9dªG,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¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V.T1 ![h,a] →
-      â\88\80X. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V.T1 â\9e¡[n,h] X â\86\92 â\93\91{p,I}V.T1 ≛ X →
-      â\88\83â\88\83T2. â¦\83G,Lâ¦\84 â\8a¢ V ![h,a] & â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ T1 ![h,a] & â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ T1 â\9e¡[n,h] T2 & T1 â\89\9b T2 & X = â\93\91{p,I}V.T2.
+      â\88\80V,T1. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V.T1 ![h,a] →
+      â\88\80X. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V.T1 â\9e¡[n,h] X â\86\92 â\93\91[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« â\8a¢ T1 â\9e¡[n,h] T2 & T1 â\89\9b T2 & X = â\93\91[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¦\83G,Lâ¦\84 ⊢ ⓐV.T1 ![h,a] →
-      â\88\80X. â¦\83G,Lâ¦\84 ⊢ ⓐV.T1 ➡[n,h] X → ⓐV.T1 ≛ X →
-      â\88\83â\88\83m,q,W,U1,T2. ad a m & â¦\83G,Lâ¦\84 â\8a¢ V ![h,a] & â¦\83G,Lâ¦\84 â\8a¢ V â\9e¡*[1,h] W & â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[m,h] â\93\9b{q}W.U1
-                   & â¦\83G,Lâ¦\84â\8a¢ T1 ![h,a] & â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓐV.T2.
+      â\88\80V,T1. â\9dªG,Lâ\9d« ⊢ ⓐV.T1 ![h,a] →
+      â\88\80X. â\9dªG,Lâ\9d« ⊢ ⓐV.T1 ➡[n,h] 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¡*[1,h] W & â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[m,h] â\93\9b[q]W.U1
+                   & â\9dªG,Lâ\9d«â\8a¢ T1 ![h,a] & â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] 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¦\83G,Lâ¦\84 ⊢ ⓝU1.T1 ![h,a] →
-      â\88\80X. â¦\83G,Lâ¦\84 ⊢ ⓝU1.T1 ➡[n,h] X → ⓝU1.T1 ≛ X →
-      â\88\83â\88\83U0,U2,T2. â¦\83G,Lâ¦\84 â\8a¢ U1 â\9e¡*[h] U0 & â¦\83G,Lâ¦\84 ⊢ T1 ➡*[1,h] U0
-                & â¦\83G,Lâ¦\84 â\8a¢ U1 ![h,a] & â¦\83G,Lâ¦\84 ⊢ U1 ➡[n,h] U2 & U1 ≛ U2
-                & â¦\83G,Lâ¦\84 â\8a¢ T1 ![h,a] & â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓝU2.T2.
+      â\88\80U1,T1. â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ![h,a] →
+      â\88\80X. â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ➡[n,h] X → ⓝU1.T1 ≛ X →
+      â\88\83â\88\83U0,U2,T2. â\9dªG,Lâ\9d« â\8a¢ U1 â\9e¡*[h] U0 & â\9dªG,Lâ\9d« ⊢ T1 ➡*[1,h] U0
+                & â\9dªG,Lâ\9d« â\8a¢ U1 ![h,a] & â\9dªG,Lâ\9d« ⊢ U1 ➡[n,h] U2 & U1 ≛ U2
+                & â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] & â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] 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¦\83G,Lâ¦\84 ⊢ X ![h,a] →
-      â\88\80V,T2. â¦\83G,Lâ¦\84 â\8a¢ X â\9e¡[n,h] â\93\91{p,I}V.T2 â\86\92 X â\89\9b â\93\91{p,I}V.T2 →
-      â\88\83â\88\83T1. â¦\83G,Lâ¦\84 â\8a¢ V ![h,a] & â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ T1 ![h,a] & â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ T1 â\9e¡[n,h] T2 & T1 â\89\9b T2 & X = â\93\91{p,I}V.T1.
+      â\88\80X. â\9dªG,Lâ\9d« ⊢ X ![h,a] →
+      â\88\80V,T2. â\9dªG,Lâ\9d« â\8a¢ X â\9e¡[n,h] â\93\91[p,I]V.T2 â\86\92 X â\89\9b â\93\91[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« â\8a¢ T1 â\9e¡[n,h] T2 & T1 â\89\9b T2 & X = â\93\91[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
@@ -127,25 +127,25 @@ qed-.
 (* Eliminators with restricted rt-transition for terms **********************)
 
 lemma cpm_teqx_ind (h) (a) (n) (G) (Q:relation3 …):
-      (∀I,L. n = 0 → Q L (⓪{I}) (⓪{I})) →
+      (∀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¦\83G,Lâ¦\84â\8a¢ V![h,a] â\86\92 â¦\83G,L.â\93\91{I}Vâ¦\84⊢T1![h,a] →
-        â\88\80T2. â¦\83G,L.â\93\91{I}Vâ¦\84 ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
-        Q (L.ⓑ{I}V) T1 T2 → Q L (ⓑ{p,I}V.T1) (ⓑ{p,I}V.T2)
+      (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 ➡[n,h] 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¦\83G,Lâ¦\84 â\8a¢ V ![h,a] â\86\92 â\88\80W. â¦\83G,Lâ¦\84 ⊢ V ➡*[1,h] W →
-        â\88\80p,T1,U1. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[m,h] â\93\9b{p}W.U1 â\86\92 â¦\83G,Lâ¦\84⊢ T1 ![h,a] →
-        â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
+        â\88\80L,V. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] â\86\92 â\88\80W. â\9dªG,Lâ\9d« ⊢ V ➡*[1,h] W →
+        â\88\80p,T1,U1. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[m,h] â\93\9b[p]W.U1 â\86\92 â\9dªG,Lâ\9d«⊢ T1 ![h,a] →
+        â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
         Q L T1 T2 → Q L (ⓐV.T1) (ⓐV.T2)
       ) →
-      (â\88\80L,U0,U1,T1. â¦\83G,Lâ¦\84 â\8a¢ U1 â\9e¡*[h] U0 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[1,h] U0 →
-        â\88\80U2. â¦\83G,Lâ¦\84 â\8a¢ U1 ![h,a] â\86\92 â¦\83G,Lâ¦\84 ⊢ U1 ➡[n,h] U2 → U1 ≛ U2 →
-        â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 ![h,a] â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
+      (â\88\80L,U0,U1,T1. â\9dªG,Lâ\9d« â\8a¢ U1 â\9e¡*[h] U0 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[1,h] U0 →
+        â\88\80U2. â\9dªG,Lâ\9d« â\8a¢ U1 ![h,a] â\86\92 â\9dªG,Lâ\9d« ⊢ U1 ➡[n,h] U2 → U1 ≛ U2 →
+        â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
         Q L U1 U2 → Q L T1 T2 → Q L (ⓝU1.T1) (ⓝU2.T2)
       ) →
-      â\88\80L,T1. â¦\83G,Lâ¦\84 ⊢ T1 ![h,a] →
-      â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 → Q L T1 T2.
+      â\88\80L,T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
+      â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] 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¦\83G,Lâ¦\84 ⊢ T1 ![h,a] →
-      â\88\80T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
-      â\88\80F,K. â¦\83F,Kâ¦\84 ⊢ T1 ➡[n,h] T2.
+      â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
+      â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
+      â\88\80F,K. â\9dªF,Kâ\9d« ⊢ T1 ➡[n,h] 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¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V.T1 ![h,a] →
-      â\88\80X. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V.T1 â\9e¡[n,h] X â\86\92 â\93\91{p,I}V.T1 ≛ X →
-      â\88\83â\88\83T2. â¦\83G,Lâ¦\84 â\8a¢ V ![h,a] & â¦\83G,L.â\93\91{I}Vâ¦\84 â\8a¢ T1 ![h,a] & â¦\83G,L.â\93§â¦\84 â\8a¢ T1 â\9e¡[n,h] T2 & T1 â\89\9b T2 & X = â\93\91{p,I}V.T2.
+      â\88\80V,T1. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V.T1 ![h,a] →
+      â\88\80X. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V.T1 â\9e¡[n,h] X â\86\92 â\93\91[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« â\8a¢ T1 â\9e¡[n,h] T2 & T1 â\89\9b T2 & X = â\93\91[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/