X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fcnv_cpm_teqx.ma;h=4a5e09ff81dce6f99cd0ff0fdcdc614a442c7a49;hp=1cc63fbae6151485247840bbf8075b679f9e0859;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

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 1cc63fbae..4a5e09ff8 100644
--- 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):
-      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡[h] T2 → T1 ≛ T2 → ⦃G,L⦄ ⊢ T1 ![h,a] → T1 = T2.
+      ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[h] T2 → T1 ≛ T2 → ❪G,L❫ ⊢ 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):
-      ∀V,T1. ⦃G,L⦄ ⊢ ⓑ{p,I}V.T1 ![h,a] →
-      ∀X. ⦃G,L⦄ ⊢ ⓑ{p,I}V.T1 ➡[n,h] X → ⓑ{p,I}V.T1 ≛ X →
-      ∃∃T2. ⦃G,L⦄ ⊢ V ![h,a] & ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ![h,a] & ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓑ{p,I}V.T2.
+      ∀V,T1. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ![h,a] →
+      ∀X. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ➡[n,h] X → ⓑ[p,I]V.T1 ≛ X →
+      ∃∃T2. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ➡[n,h] 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):
-      ∀V,T1. ⦃G,L⦄ ⊢ ⓐV.T1 ![h,a] →
-      ∀X. ⦃G,L⦄ ⊢ ⓐV.T1 ➡[n,h] X → ⓐV.T1 ≛ X →
-      ∃∃m,q,W,U1,T2. ad a m & ⦃G,L⦄ ⊢ V ![h,a] & ⦃G,L⦄ ⊢ V ➡*[1,h] W & ⦃G,L⦄ ⊢ T1 ➡*[m,h] ⓛ{q}W.U1
-                   & ⦃G,L⦄⊢ T1 ![h,a] & ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓐV.T2.
+      ∀V,T1. ❪G,L❫ ⊢ ⓐV.T1 ![h,a] →
+      ∀X. ❪G,L❫ ⊢ ⓐV.T1 ➡[n,h] X → ⓐV.T1 ≛ X →
+      ∃∃m,q,W,U1,T2. ad a m & ❪G,L❫ ⊢ V ![h,a] & ❪G,L❫ ⊢ V ➡*[1,h] W & ❪G,L❫ ⊢ T1 ➡*[m,h] ⓛ[q]W.U1
+                   & ❪G,L❫⊢ T1 ![h,a] & ❪G,L❫ ⊢ 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):
-      ∀U1,T1. ⦃G,L⦄ ⊢ ⓝU1.T1 ![h,a] →
-      ∀X. ⦃G,L⦄ ⊢ ⓝU1.T1 ➡[n,h] X → ⓝU1.T1 ≛ X →
-      ∃∃U0,U2,T2. ⦃G,L⦄ ⊢ U1 ➡*[h] U0 & ⦃G,L⦄ ⊢ T1 ➡*[1,h] U0
-                & ⦃G,L⦄ ⊢ U1 ![h,a] & ⦃G,L⦄ ⊢ U1 ➡[n,h] U2 & U1 ≛ U2
-                & ⦃G,L⦄ ⊢ T1 ![h,a] & ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓝU2.T2.
+      ∀U1,T1. ❪G,L❫ ⊢ ⓝU1.T1 ![h,a] →
+      ∀X. ❪G,L❫ ⊢ ⓝU1.T1 ➡[n,h] X → ⓝU1.T1 ≛ X →
+      ∃∃U0,U2,T2. ❪G,L❫ ⊢ U1 ➡*[h] U0 & ❪G,L❫ ⊢ T1 ➡*[1,h] U0
+                & ❪G,L❫ ⊢ U1 ![h,a] & ❪G,L❫ ⊢ U1 ➡[n,h] U2 & U1 ≛ U2
+                & ❪G,L❫ ⊢ T1 ![h,a] & ❪G,L❫ ⊢ 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):
-      ∀X. ⦃G,L⦄ ⊢ X ![h,a] →
-      ∀V,T2. ⦃G,L⦄ ⊢ X ➡[n,h] ⓑ{p,I}V.T2 → X ≛ ⓑ{p,I}V.T2 →
-      ∃∃T1. ⦃G,L⦄ ⊢ V ![h,a] & ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ![h,a] & ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓑ{p,I}V.T1.
+      ∀X. ❪G,L❫ ⊢ X ![h,a] →
+      ∀V,T2. ❪G,L❫ ⊢ X ➡[n,h] ⓑ[p,I]V.T2 → X ≛ ⓑ[p,I]V.T2 →
+      ∃∃T1. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ➡[n,h] 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
@@ -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))) →
-      (∀p,I,L,V,T1. ⦃G,L⦄⊢ V![h,a] → ⦃G,L.ⓑ{I}V⦄⊢T1![h,a] →
-        ∀T2. ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
-        Q (L.ⓑ{I}V) T1 T2 → Q L (ⓑ{p,I}V.T1) (ⓑ{p,I}V.T2)
+      (∀p,I,L,V,T1. ❪G,L❫⊢ V![h,a] → ❪G,L.ⓑ[I]V❫⊢T1![h,a] →
+        ∀T2. ❪G,L.ⓑ[I]V❫ ⊢ 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 →
-        ∀L,V. ⦃G,L⦄ ⊢ V ![h,a] → ∀W. ⦃G,L⦄ ⊢ V ➡*[1,h] W →
-        ∀p,T1,U1. ⦃G,L⦄ ⊢ T1 ➡*[m,h] ⓛ{p}W.U1 → ⦃G,L⦄⊢ T1 ![h,a] →
-        ∀T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
+        ∀L,V. ❪G,L❫ ⊢ V ![h,a] → ∀W. ❪G,L❫ ⊢ V ➡*[1,h] W →
+        ∀p,T1,U1. ❪G,L❫ ⊢ T1 ➡*[m,h] ⓛ[p]W.U1 → ❪G,L❫⊢ T1 ![h,a] →
+        ∀T2. ❪G,L❫ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
         Q L T1 T2 → Q L (ⓐV.T1) (ⓐV.T2)
       ) →
-      (∀L,U0,U1,T1. ⦃G,L⦄ ⊢ U1 ➡*[h] U0 → ⦃G,L⦄ ⊢ T1 ➡*[1,h] U0 →
-        ∀U2. ⦃G,L⦄ ⊢ U1 ![h,a] → ⦃G,L⦄ ⊢ U1 ➡[n,h] U2 → U1 ≛ U2 →
-        ∀T2. ⦃G,L⦄ ⊢ T1 ![h,a] → ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
+      (∀L,U0,U1,T1. ❪G,L❫ ⊢ U1 ➡*[h] U0 → ❪G,L❫ ⊢ T1 ➡*[1,h] U0 →
+        ∀U2. ❪G,L❫ ⊢ U1 ![h,a] → ❪G,L❫ ⊢ U1 ➡[n,h] U2 → U1 ≛ U2 →
+        ∀T2. ❪G,L❫ ⊢ T1 ![h,a] → ❪G,L❫ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
         Q L U1 U2 → Q L T1 T2 → Q L (ⓝU1.T1) (ⓝU2.T2)
       ) →
-      ∀L,T1. ⦃G,L⦄ ⊢ T1 ![h,a] →
-      ∀T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 → Q L T1 T2.
+      ∀L,T1. ❪G,L❫ ⊢ T1 ![h,a] →
+      ∀T2. ❪G,L❫ ⊢ 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):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] →
-      ∀T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
-      ∀F,K. ⦃F,K⦄ ⊢ T1 ➡[n,h] T2.
+      ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
+      ∀T2. ❪G,L❫ ⊢ T1 ➡[n,h] T2 → T1 ≛ T2 →
+      ∀F,K. ❪F,K❫ ⊢ 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):
-      ∀V,T1. ⦃G,L⦄ ⊢ ⓑ{p,I}V.T1 ![h,a] →
-      ∀X. ⦃G,L⦄ ⊢ ⓑ{p,I}V.T1 ➡[n,h] X → ⓑ{p,I}V.T1 ≛ X →
-      ∃∃T2. ⦃G,L⦄ ⊢ V ![h,a] & ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ![h,a] & ⦃G,L.ⓧ⦄ ⊢ T1 ➡[n,h] T2 & T1 ≛ T2 & X = ⓑ{p,I}V.T2.
+      ∀V,T1. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ![h,a] →
+      ∀X. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ➡[n,h] X → ⓑ[p,I]V.T1 ≛ X →
+      ∃∃T2. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓧ❫ ⊢ T1 ➡[n,h] 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/