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=51d06a1bd17c56029d97bd970f0388c95749707f;hp=23287638d8a15802812e79d3d9f92191303c5f19;hb=b118146b97959e6a6dde18fdd014b8e1e676a2d1;hpb=613d8642b1154dde0c026cbdcd96568910198251

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 23287638d..51d06a1bd 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
@@ -24,13 +24,13 @@ 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,0] T2 → T1 ≛ T2 → ❪G,L❫ ⊢ T1 ![h,a] → T1 = T2.
+      ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[h,0] 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
-  lapply (teqx_inv_lref1 … H1) -H1 #H destruct //
+  lapply (teqg_inv_lref1 … H1) -H1 #H destruct //
 | #I #G #K #T2 #X2 #i #_ #_ #_ #H1 #_ -a -I -G -K -T2
-  lapply (teqx_inv_lref1 … H1) -H1 #H destruct //
+  lapply (teqg_inv_lref1 … H1) -H1 #H destruct //
 | #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #H1 #H2
   elim (teqx_inv_pair1 … H1) -H1 #V0 #T0 #HV0 #HT0 #H destruct
   elim (cnv_inv_bind … H2) -H2 #HV1 #HT1
@@ -46,7 +46,7 @@ lemma cnv_cpr_teqx_fwd_refl (h) (a) (G) (L):
 | #G #L #U #T1 #T2 #HT12 #_ #H1 #H2
   elim (cnv_fpbg_refl_false … H2) -a
   @(fpbg_teqx_div … H1) -H1
-  /3 width=7 by cpm_tneqx_cpm_fpbg, cpm_eps, teqx_inv_pair_xy_y/
+  /3 width=7 by cpm_tneqx_cpm_fpbg, cpm_eps, teqg_inv_pair_xy_y/
 | #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #H1 #_
   elim (teqx_inv_pair … H1) -H1 #H #_ #_ destruct
 | #p #G #L #V1 #V2 #X2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H1 #_
@@ -56,8 +56,8 @@ 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 ➡[h,n] X → ⓑ[p,I]V.T1 ≛ X →
-      ∃∃T2. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ➡[h,n] T2 & T1 ≛ T2 & X = ⓑ[p,I]V.T2.
+      ∀X. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ➡[h,n] X → ⓑ[p,I]V.T1 ≅ X →
+      ∃∃T2. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ 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
@@ -74,9 +74,9 @@ 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 ➡[h,n] X → ⓐV.T1 ≛ X →
+      ∀X. ❪G,L❫ ⊢ ⓐV.T1 ➡[h,n] X → ⓐV.T1 ≅ X →
       ∃∃m,q,W,U1,T2. ad a m & ❪G,L❫ ⊢ V ![h,a] & ❪G,L❫ ⊢ V ➡*[h,1] W & ❪G,L❫ ⊢ T1 ➡*[h,m] ⓛ[q]W.U1
-                   & ❪G,L❫⊢ T1 ![h,a] & ❪G,L❫ ⊢ T1 ➡[h,n] T2 & T1 ≛ T2 & X = ⓐV.T2.
+                   & ❪G,L❫⊢ T1 ![h,a] & ❪G,L❫ ⊢ 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
@@ -93,10 +93,10 @@ 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 ➡[h,n] X → ⓝU1.T1 ≛ X →
+      ∀X. ❪G,L❫ ⊢ ⓝU1.T1 ➡[h,n] X → ⓝU1.T1 ≅ X →
       ∃∃U0,U2,T2. ❪G,L❫ ⊢ U1 ➡*[h,0] U0 & ❪G,L❫ ⊢ T1 ➡*[h,1] U0
-                & ❪G,L❫ ⊢ U1 ![h,a] & ❪G,L❫ ⊢ U1 ➡[h,n] U2 & U1 ≛ U2
-                & ❪G,L❫ ⊢ T1 ![h,a] & ❪G,L❫ ⊢ T1 ➡[h,n] T2 & T1 ≛ T2 & X = ⓝU2.T2.
+                & ❪G,L❫ ⊢ U1 ![h,a] & ❪G,L❫ ⊢ U1 ➡[h,n] U2 & U1 ≅ U2
+                & ❪G,L❫ ⊢ T1 ![h,a] & ❪G,L❫ ⊢ 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
@@ -106,18 +106,18 @@ elim (cpm_inv_cast1 … H1) -H1 [ * || * ]
 | #HT1X
   elim (cnv_fpbg_refl_false … H0) -a
   @(fpbg_teqx_div … H2) -H2
-  /3 width=7 by cpm_tneqx_cpm_fpbg, cpm_eps, teqx_inv_pair_xy_y/
+  /3 width=7 by cpm_tneqx_cpm_fpbg, cpm_eps, teqg_inv_pair_xy_y/
 | #m #HU1X #H destruct
   elim (cnv_fpbg_refl_false … H0) -a
   @(fpbg_teqx_div … H2) -H2
-  /3 width=7 by cpm_tneqx_cpm_fpbg, cpm_ee, teqx_inv_pair_xy_x/
+  /3 width=7 by cpm_tneqx_cpm_fpbg, cpm_ee, teqg_inv_pair_xy_x/
 ]
 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 ➡[h,n] ⓑ[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 ➡[h,n] T2 & T1 ≛ T2 & X = ⓑ[p,I]V.T1.
+      ∀V,T2. ❪G,L❫ ⊢ X ➡[h,n] ⓑ[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 ➡[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
@@ -130,22 +130,22 @@ 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))) →
       (∀p,I,L,V,T1. ❪G,L❫⊢ V![h,a] → ❪G,L.ⓑ[I]V❫⊢T1![h,a] →
-        ∀T2. ❪G,L.ⓑ[I]V❫ ⊢ T1 ➡[h,n] T2 → T1 ≛ T2 →
+        ∀T2. ❪G,L.ⓑ[I]V❫ ⊢ 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 →
         ∀L,V. ❪G,L❫ ⊢ V ![h,a] → ∀W. ❪G,L❫ ⊢ V ➡*[h,1] W →
         ∀p,T1,U1. ❪G,L❫ ⊢ T1 ➡*[h,m] ⓛ[p]W.U1 → ❪G,L❫⊢ T1 ![h,a] →
-        ∀T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 → T1 ≛ T2 →
+        ∀T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
         Q L T1 T2 → Q L (ⓐV.T1) (ⓐV.T2)
       ) →
       (∀L,U0,U1,T1. ❪G,L❫ ⊢ U1 ➡*[h,0] U0 → ❪G,L❫ ⊢ T1 ➡*[h,1] U0 →
-        ∀U2. ❪G,L❫ ⊢ U1 ![h,a] → ❪G,L❫ ⊢ U1 ➡[h,n] U2 → U1 ≛ U2 →
-        ∀T2. ❪G,L❫ ⊢ T1 ![h,a] → ❪G,L❫ ⊢ T1 ➡[h,n] T2 → T1 ≛ T2 →
+        ∀U2. ❪G,L❫ ⊢ U1 ![h,a] → ❪G,L❫ ⊢ U1 ➡[h,n] U2 → U1 ≅ U2 →
+        ∀T2. ❪G,L❫ ⊢ T1 ![h,a] → ❪G,L❫ ⊢ T1 ➡[h,n] 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 ➡[h,n] T2 → T1 ≛ T2 → Q L T1 T2.
+      ∀T2. ❪G,L❫ ⊢ 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
@@ -171,7 +171,7 @@ qed-.
 
 lemma cpm_teqx_free (h) (a) (n) (G) (L):
       ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
-      ∀T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 → T1 ≛ T2 →
+      ∀T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 → T1 ≅ T2 →
       ∀F,K. ❪F,K❫ ⊢ T1 ➡[h,n] T2.
 #h #a #n #G #L #T1 #H0 #T2 #H1 #H2
 @(cpm_teqx_ind … H0 … H1 H2) -L -T1 -T2
@@ -190,8 +190,8 @@ qed-.
 
 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 ➡[h,n] X → ⓑ[p,I]V.T1 ≛ X →
-      ∃∃T2. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓧ❫ ⊢ T1 ➡[h,n] T2 & T1 ≛ T2 & X = ⓑ[p,I]V.T2.
+      ∀X. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ➡[h,n] X → ⓑ[p,I]V.T1 ≅ X →
+      ∃∃T2. ❪G,L❫ ⊢ V ![h,a] & ❪G,L.ⓑ[I]V❫ ⊢ T1 ![h,a] & ❪G,L.ⓧ❫ ⊢ 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/