update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
index 6de11fe1620e2e1a6bc251ebf708355b8fd54546..eb8d953a23c649d61bc13a90853971f41297036e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
@@ -22,11 +22,11 @@ include "basic_2/dynamic/nta.ma".
 (* Properties based on preservation *****************************************)
 
 lemma cnv_cpms_nta (h) (a) (G) (L):
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a] â\86\92 â\88\80U.â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[1,h] U â\86\92 â¦\83G,Lâ¦\84 ⊢ T :[h,a] U.
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\88\80U.â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[1,h] U â\86\92 â\9dªG,Lâ\9d« ⊢ T :[h,a] U.
 /3 width=4 by cnv_cast, cnv_cpms_trans/ qed.
 
 lemma cnv_nta_sn (h) (a) (G) (L):
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a] â\86\92 â\88\83U. â¦\83G,Lâ¦\84 ⊢ T :[h,a] U.
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\88\83U. â\9dªG,Lâ\9d« ⊢ T :[h,a] U.
 #h #a #G #L #T #HT
 elim (cnv_fwd_cpm_SO … HT) #U #HTU
 /4 width=2 by cnv_cpms_nta, cpm_cpms, ex_intro/
@@ -34,18 +34,18 @@ qed-.
 
 (* Basic_1: was: ty3_typecheck *)
 lemma nta_typecheck (h) (a) (G) (L):
-      â\88\80T,U. â¦\83G,Lâ¦\84 â\8a¢ T :[h,a] U â\86\92 â\88\83T0. â¦\83G,Lâ¦\84 ⊢ ⓝU.T :[h,a] T0.
+      â\88\80T,U. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U â\86\92 â\88\83T0. â\9dªG,Lâ\9d« ⊢ ⓝU.T :[h,a] T0.
 /3 width=1 by cnv_cast, cnv_nta_sn/ qed-.
 
 (* Basic_1: was: ty3_correct *)
 (* Basic_2A1: was: ntaa_fwd_correct *)
 lemma nta_fwd_correct (h) (a) (G) (L):
-      â\88\80T,U. â¦\83G,Lâ¦\84 â\8a¢ T :[h,a] U â\86\92 â\88\83T0. â¦\83G,Lâ¦\84 ⊢ U :[h,a] T0.
+      â\88\80T,U. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U â\86\92 â\88\83T0. â\9dªG,Lâ\9d« ⊢ U :[h,a] T0.
 /3 width=2 by nta_fwd_cnv_dx, cnv_nta_sn/ qed-.
 
 lemma nta_pure_cnv (h) (G) (L):
-      â\88\80T,U. â¦\83G,Lâ¦\84 ⊢ T :[h,𝛚] U →
-      â\88\80V. â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.U ![h,ð\9d\9b\9a] â\86\92 â¦\83G,Lâ¦\84 ⊢ ⓐV.T :[h,𝛚] ⓐV.U.
+      â\88\80T,U. â\9dªG,Lâ\9d« ⊢ T :[h,𝛚] U →
+      â\88\80V. â\9dªG,Lâ\9d« â\8a¢ â\93\90V.U ![h,ð\9d\9b\9a] â\86\92 â\9dªG,Lâ\9d« ⊢ ⓐV.T :[h,𝛚] ⓐV.U.
 #h #G #L #T #U #H1 #V #H2
 elim (cnv_inv_cast … H1) -H1 #X0 #HU #HT #HUX0 #HTX0
 elim (cnv_inv_appl … H2) #n #p #X1 #X2 #_ #HV #_ #HVX1 #HUX2
@@ -58,16 +58,16 @@ qed.
 
 (* Basic_1: uses: ty3_sred_wcpr0_pr0 *)
 lemma nta_cpr_conf_lpr (h) (a) (G):
-      â\88\80L1,T1,U. â¦\83G,L1â¦\84 â\8a¢ T1 :[h,a] U â\86\92 â\88\80T2. â¦\83G,L1â¦\84 ⊢ T1 ➡[h] T2 →
-      â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G,L2â¦\84 ⊢ T2 :[h,a] U.
+      â\88\80L1,T1,U. â\9dªG,L1â\9d« â\8a¢ T1 :[h,a] U â\86\92 â\88\80T2. â\9dªG,L1â\9d« ⊢ T1 ➡[h] T2 →
+      â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T2 :[h,a] U.
 #h #a #G #L1 #T1 #U #H #T2 #HT12 #L2 #HL12
 /3 width=6 by cnv_cpm_trans_lpr, cpm_cast/
 qed-.
 
 (* Basic_1: uses: ty3_sred_pr2 ty3_sred_pr0 *)
 lemma nta_cpr_conf (h) (a) (G) (L):
-      â\88\80T1,U. â¦\83G,Lâ¦\84 ⊢ T1 :[h,a] U →
-      â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 :[h,a] U.
+      â\88\80T1,U. â\9dªG,Lâ\9d« ⊢ T1 :[h,a] U →
+      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T2 :[h,a] U.
 #h #a #G #L #T1 #U #H #T2 #HT12
 /3 width=6 by cnv_cpm_trans, cpm_cast/
 qed-.
@@ -75,24 +75,24 @@ qed-.
 (* Note: this is the preservation property *)
 (* Basic_1: uses: ty3_sred_pr3 ty3_sred_pr1 *)
 lemma nta_cprs_conf (h) (a) (G) (L):
-      â\88\80T1,U. â¦\83G,Lâ¦\84 ⊢ T1 :[h,a] U →
-      â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 :[h,a] U.
+      â\88\80T1,U. â\9dªG,Lâ\9d« ⊢ T1 :[h,a] U →
+      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T2 :[h,a] U.
 #h #a #G #L #T1 #U #H #T2 #HT12
 /3 width=6 by cnv_cpms_trans, cpms_cast/
 qed-.
 
 (* Basic_1: uses: ty3_cred_pr2 *)
 lemma nta_lpr_conf (h) (a) (G):
-      â\88\80L1,T,U. â¦\83G,L1â¦\84 ⊢ T :[h,a] U →
-      â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G,L2â¦\84 ⊢ T :[h,a] U.
+      â\88\80L1,T,U. â\9dªG,L1â\9d« ⊢ T :[h,a] U →
+      â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T :[h,a] U.
 #h #a #G #L1 #T #U #HTU #L2 #HL12
 /2 width=3 by cnv_lpr_trans/
 qed-.
 
 (* Basic_1: uses: ty3_cred_pr3 *)
 lemma nta_lprs_conf (h) (a) (G):
-      â\88\80L1,T,U. â¦\83G,L1â¦\84 ⊢ T :[h,a] U →
-      â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â\9e¡*[h] L2 â\86\92 â¦\83G,L2â¦\84 ⊢ T :[h,a] U.
+      â\88\80L1,T,U. â\9dªG,L1â\9d« ⊢ T :[h,a] U →
+      â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡*[h] L2 â\86\92 â\9dªG,L2â\9d« ⊢ T :[h,a] U.
 #h #a #G #L1 #T #U #HTU #L2 #HL12
 /2 width=3 by cnv_lprs_trans/
 qed-.
@@ -100,8 +100,8 @@ qed-.
 (* Inversion lemmas based on preservation ***********************************)
 
 lemma nta_inv_ldef_sn (h) (a) (G) (K) (V):
-      â\88\80X2. â¦\83G,K.â\93\93Vâ¦\84 ⊢ #0 :[h,a] X2 →
-      â\88\83â\88\83W,U. â¦\83G,Kâ¦\84 â\8a¢ V :[h,a] W & â\87§*[1] W â\89\98 U & â¦\83G,K.â\93\93Vâ¦\84 â\8a¢ U â¬\8c*[h] X2 & â¦\83G,K.â\93\93Vâ¦\84 ⊢ X2 ![h,a].
+      â\88\80X2. â\9dªG,K.â\93\93Vâ\9d« ⊢ #0 :[h,a] X2 →
+      â\88\83â\88\83W,U. â\9dªG,Kâ\9d« â\8a¢ V :[h,a] W & â\87§*[1] W â\89\98 U & â\9dªG,K.â\93\93Vâ\9d« â\8a¢ U â¬\8c*[h] X2 & â\9dªG,K.â\93\93Vâ\9d« ⊢ X2 ![h,a].
 #h #a #G #Y #X #X2 #H
 elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
 elim (cnv_inv_zero … H1) -H1 #Z #K #V #HV #H destruct
@@ -113,8 +113,8 @@ elim (cpms_inv_delta_sn … H2) -H2 *
 qed-.
 
 lemma nta_inv_lref_sn (h) (a) (G) (L):
-      â\88\80X2,i. â¦\83G,Lâ¦\84 ⊢ #↑i :[h,a] X2 →
-      â\88\83â\88\83I,K,T2,U2. â¦\83G,Kâ¦\84 â\8a¢ #i :[h,a] T2 & â\87§*[1] T2 â\89\98 U2 & â¦\83G,K.â\93\98{I}â¦\84 â\8a¢ U2 â¬\8c*[h] X2 & â¦\83G,K.â\93\98{I}â¦\84 â\8a¢ X2 ![h,a] & L = K.â\93\98{I}.
+      â\88\80X2,i. â\9dªG,Lâ\9d« ⊢ #↑i :[h,a] X2 →
+      â\88\83â\88\83I,K,T2,U2. â\9dªG,Kâ\9d« â\8a¢ #i :[h,a] T2 & â\87§*[1] T2 â\89\98 U2 & â\9dªG,K.â\93\98[I]â\9d« â\8a¢ U2 â¬\8c*[h] X2 & â\9dªG,K.â\93\98[I]â\9d« â\8a¢ X2 ![h,a] & L = K.â\93\98[I].
 #h #a #G #L #X2 #i #H
 elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
 elim (cnv_inv_lref … H1) -H1 #I #K #Hi #H destruct
@@ -126,9 +126,9 @@ elim (cpms_inv_lref_sn … H2) -H2 *
 qed-.
 
 lemma nta_inv_lref_sn_drops_cnv (h) (a) (G) (L):
-      â\88\80X2,i. â¦\83G,Lâ¦\84 ⊢ #i :[h,a] X2 →
-      â\88¨â\88¨ â\88\83â\88\83K,V,W,U. â\87©*[i] L â\89\98 K.â\93\93V & â¦\83G,Kâ¦\84 â\8a¢ V :[h,a] W & â\87§*[â\86\91i] W â\89\98 U & â¦\83G,Lâ¦\84 â\8a¢ U â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,a]
-       | â\88\83â\88\83K,W,U. â\87©*[i] L â\89\98 K. â\93\9bW & â¦\83G,Kâ¦\84 â\8a¢ W ![h,a] & â\87§*[â\86\91i] W â\89\98 U & â¦\83G,Lâ¦\84 â\8a¢ U â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,a].
+      â\88\80X2,i. â\9dªG,Lâ\9d« ⊢ #i :[h,a] X2 →
+      â\88¨â\88¨ â\88\83â\88\83K,V,W,U. â\87©*[i] L â\89\98 K.â\93\93V & â\9dªG,Kâ\9d« â\8a¢ V :[h,a] W & â\87§*[â\86\91i] W â\89\98 U & â\9dªG,Lâ\9d« â\8a¢ U â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,a]
+       | â\88\83â\88\83K,W,U. â\87©*[i] L â\89\98 K. â\93\9bW & â\9dªG,Kâ\9d« â\8a¢ W ![h,a] & â\87§*[â\86\91i] W â\89\98 U & â\9dªG,Lâ\9d« â\8a¢ U â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,a].
 #h #a #G #L #X2 #i #H
 elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
 elim (cnv_inv_lref_drops … H1) -H1 #I #K #V #HLK #HV
@@ -139,7 +139,7 @@ elim (cpms_inv_lref1_drops … H2) -H2 *
   /4 width=8 by cnv_cpms_nta, cpcs_cprs_sn, ex5_4_intro, or_introl/
 | #n #Y #X #U #H #HVU #HUX1 #H0 destruct
   lapply (drops_mono … H … HLK) -H #H destruct
-  elim (lifts_total V (ð\9d\90\94â\9d´â\86\91iâ\9dµ)) #W #HVW
+  elim (lifts_total V (ð\9d\90\94â\9d¨â\86\91iâ\9d©)) #W #HVW
   lapply (cpms_lifts_bi … HVU (Ⓣ) … L … HVW … HUX1) -U
   [ /2 width=2 by drops_isuni_fwd_drop2/ ] #HWX1
   /4 width=9 by cprs_div, ex5_3_intro, or_intror/
@@ -147,8 +147,8 @@ elim (cpms_inv_lref1_drops … H2) -H2 *
 qed-.
 
 lemma nta_inv_bind_sn_cnv (h) (a) (p) (I) (G) (K) (X2):
-      â\88\80V,T. â¦\83G,Kâ¦\84 â\8a¢ â\93\91{p,I}V.T :[h,a] X2 →
-      â\88\83â\88\83U. â¦\83G,Kâ¦\84 â\8a¢ V ![h,a] & â¦\83G,K.â\93\91{I}Vâ¦\84 â\8a¢ T :[h,a] U & â¦\83G,Kâ¦\84 â\8a¢ â\93\91{p,I}V.U â¬\8c*[h] X2 & â¦\83G,Kâ¦\84 ⊢ X2 ![h,a].
+      â\88\80V,T. â\9dªG,Kâ\9d« â\8a¢ â\93\91[p,I]V.T :[h,a] X2 →
+      â\88\83â\88\83U. â\9dªG,Kâ\9d« â\8a¢ V ![h,a] & â\9dªG,K.â\93\91[I]Vâ\9d« â\8a¢ T :[h,a] U & â\9dªG,Kâ\9d« â\8a¢ â\93\91[p,I]V.U â¬\8c*[h] X2 & â\9dªG,Kâ\9d« ⊢ X2 ![h,a].
 #h #a #p * #G #K #X2 #V #T #H
 elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
 elim (cnv_inv_bind … H1) -H1 #HV #HT
@@ -165,8 +165,8 @@ qed-.
 
 (* Basic_1: uses: ty3_gen_appl *)
 lemma nta_inv_appl_sn (h) (G) (L) (X2):
-      â\88\80V,T. â¦\83G,Lâ¦\84 ⊢ ⓐV.T :[h,𝟐] X2 →
-      â\88\83â\88\83p,W,U. â¦\83G,Lâ¦\84 â\8a¢ V :[h,ð\9d\9f\90] W & â¦\83G,Lâ¦\84 â\8a¢ T :[h,ð\9d\9f\90] â\93\9b{p}W.U & â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\9b{p}W.U â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,𝟐].
+      â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ⓐV.T :[h,𝟐] X2 →
+      â\88\83â\88\83p,W,U. â\9dªG,Lâ\9d« â\8a¢ V :[h,ð\9d\9f\90] W & â\9dªG,Lâ\9d« â\8a¢ T :[h,ð\9d\9f\90] â\93\9b[p]W.U & â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\9b[p]W.U â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,𝟐].
 #h #G #L #X2 #V #T #H
 elim (cnv_inv_cast … H) -H #X #HX2 #H1 #HX2 #H2
 elim (cnv_inv_appl … H1) #n #p #W #U #H <H -n #HV #HT #HVW #HTU
@@ -175,16 +175,16 @@ qed-.
 
 (* Basic_2A1: uses: nta_fwd_pure1 *)
 lemma nta_inv_pure_sn_cnv (h) (G) (L) (X2):
-      â\88\80V,T. â¦\83G,Lâ¦\84 ⊢ ⓐV.T :[h,𝛚] X2 →
-      â\88¨â\88¨ â\88\83â\88\83p,W,U. â¦\83G,Lâ¦\84 â\8a¢ V :[h,ð\9d\9b\9a] W & â¦\83G,Lâ¦\84 â\8a¢ T :[h,ð\9d\9b\9a] â\93\9b{p}W.U & â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\9b{p}W.U â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,𝛚]
-       | â\88\83â\88\83U. â¦\83G,Lâ¦\84 â\8a¢ T :[h,ð\9d\9b\9a] U & â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.U ![h,ð\9d\9b\9a] & â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.U â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,𝛚].
+      â\88\80V,T. â\9dªG,Lâ\9d« ⊢ ⓐV.T :[h,𝛚] X2 →
+      â\88¨â\88¨ â\88\83â\88\83p,W,U. â\9dªG,Lâ\9d« â\8a¢ V :[h,ð\9d\9b\9a] W & â\9dªG,Lâ\9d« â\8a¢ T :[h,ð\9d\9b\9a] â\93\9b[p]W.U & â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\9b[p]W.U â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,𝛚]
+       | â\88\83â\88\83U. â\9dªG,Lâ\9d« â\8a¢ T :[h,ð\9d\9b\9a] U & â\9dªG,Lâ\9d« â\8a¢ â\93\90V.U ![h,ð\9d\9b\9a] & â\9dªG,Lâ\9d« â\8a¢ â\93\90V.U â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,𝛚].
 #h #G #L #X2 #V #T #H
 elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H
 elim (cnv_inv_appl … H1) * [| #n ] #p #W0 #T0 #Hn #HV #HT #HW0 #HT0
 [ lapply (cnv_cpms_trans … HT … HT0) #H0
   elim (cnv_inv_bind … H0) -H0 #_ #HU
   elim (cnv_fwd_cpm_SO … HU) #U0 #HU0 -HU
-  lapply (cpms_step_dx … HT0 1 (ⓛ{p}W0.U0) ?) -HT0 [ /2 width=1 by cpm_bind/ ] #HT0
+  lapply (cpms_step_dx … HT0 1 (ⓛ[p]W0.U0) ?) -HT0 [ /2 width=1 by cpm_bind/ ] #HT0
   lapply (cpms_appl_dx … V V … HT0) [ // ] #HTU0
   lapply (cnv_cpms_conf_eq … H1 … HTU0 … H) -H1 -H -HTU0 #HU0X1
   /4 width=8 by cnv_cpms_nta, cpcs_cprs_div, ex4_3_intro, or_introl/
@@ -202,8 +202,8 @@ qed-.
 
 (* Basic_2A1: uses: nta_inv_cast1 *)
 lemma nta_inv_cast_sn (h) (a) (G) (L) (X2):
-      â\88\80U,T. â¦\83G,Lâ¦\84 ⊢ ⓝU.T :[h,a] X2 →
-      â\88§â\88§ â¦\83G,Lâ¦\84 â\8a¢ T :[h,a] U & â¦\83G,Lâ¦\84 â\8a¢ U â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,a].
+      â\88\80U,T. â\9dªG,Lâ\9d« ⊢ ⓝU.T :[h,a] X2 →
+      â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U & â\9dªG,Lâ\9d« â\8a¢ U â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,a].
 #h #a #G #L #X2 #U #T #H
 elim (cnv_inv_cast … H) -H #X0 #HX2 #H1 #HX20 #H2
 elim (cnv_inv_cast … H1) #X #HU #HT #HUX #HTX
@@ -221,8 +221,8 @@ qed-.
 
 (* Basic_1: uses: ty3_gen_cast *)
 lemma nta_inv_cast_sn_old (h) (a) (G) (L) (X2):
-      â\88\80T0,T1. â¦\83G,Lâ¦\84 ⊢ ⓝT1.T0 :[h,a] X2 →
-      â\88\83â\88\83T2. â¦\83G,Lâ¦\84 â\8a¢ T0 :[h,a] T1 & â¦\83G,Lâ¦\84 â\8a¢ T1 :[h,a] T2 & â¦\83G,Lâ¦\84 â\8a¢ â\93\9dT2.T1 â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,a].
+      â\88\80T0,T1. â\9dªG,Lâ\9d« ⊢ ⓝT1.T0 :[h,a] X2 →
+      â\88\83â\88\83T2. â\9dªG,Lâ\9d« â\8a¢ T0 :[h,a] T1 & â\9dªG,Lâ\9d« â\8a¢ T1 :[h,a] T2 & â\9dªG,Lâ\9d« â\8a¢ â\93\9dT2.T1 â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,a].
 #h #a #G #L #X2 #T0 #T1 #H
 elim (cnv_inv_cast … H) -H #X0 #HX2 #H1 #HX20 #H2
 elim (cnv_inv_cast … H1) #X #HT1 #HT0 #HT1X #HT0X
@@ -242,11 +242,11 @@ elim (cpms_inv_cast1 … H2) -H2 [ * || * ]
 qed-.
 
 (* Basic_1: uses: ty3_gen_lift *)
-(* Note: "â¦\83G, Lâ¦\84 â\8a¢ U2 â¬\8c*[h] X2" can be "â¦\83G, Lâ¦\84 ⊢ X2 ➡*[h] U2" *)
+(* Note: "â\9dªG, Lâ\9d« â\8a¢ U2 â¬\8c*[h] X2" can be "â\9dªG, Lâ\9d« ⊢ X2 ➡*[h] U2" *)
 lemma nta_inv_lifts_sn (h) (a) (G):
-      â\88\80L,T2,X2. â¦\83G,Lâ¦\84 ⊢ T2 :[h,a] X2 →
+      â\88\80L,T2,X2. â\9dªG,Lâ\9d« ⊢ T2 :[h,a] X2 →
       ∀b,f,K. ⇩*[b,f] L ≘ K → ∀T1. ⇧*[f] T1 ≘ T2 →
-      â\88\83â\88\83U1,U2. â¦\83G,Kâ¦\84 â\8a¢ T1 :[h,a] U1 & â\87§*[f] U1 â\89\98 U2 & â¦\83G,Lâ¦\84 â\8a¢ U2 â¬\8c*[h] X2 & â¦\83G,Lâ¦\84 ⊢ X2 ![h,a].
+      â\88\83â\88\83U1,U2. â\9dªG,Kâ\9d« â\8a¢ T1 :[h,a] U1 & â\87§*[f] U1 â\89\98 U2 & â\9dªG,Lâ\9d« â\8a¢ U2 â¬\8c*[h] X2 & â\9dªG,Lâ\9d« ⊢ X2 ![h,a].
 #h #a #G #L #T2 #X2 #H #b #f #K #HLK #T1 #HT12
 elim (cnv_inv_cast … H) -H #U2 #HX2 #HT2 #HXU2 #HTU2
 lapply (cnv_inv_lifts … HT2 … HLK … HT12) -HT2 #HT1
@@ -258,7 +258,7 @@ qed-.
 
 (* Basic_1: was: ty3_unique *)
 theorem nta_mono (h) (a) (G) (L) (T):
-        â\88\80U1. â¦\83G,Lâ¦\84 â\8a¢ T :[h,a] U1 â\86\92 â\88\80U2. â¦\83G,Lâ¦\84 â\8a¢ T :[h,a] U2 â\86\92 â¦\83G,Lâ¦\84  ⊢ U1 ⬌*[h] U2.
+        â\88\80U1. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U1 â\86\92 â\88\80U2. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U2 â\86\92 â\9dªG,Lâ\9d«  ⊢ U1 ⬌*[h] U2.
 #h #a #G #L #T #U1 #H1 #U2 #H2
 elim (cnv_inv_cast … H1) -H1 #X1 #_ #_ #HUX1 #HTX1
 elim (cnv_inv_cast … H2) -H2 #X2 #_ #HT #HUX2 #HTX2
@@ -270,8 +270,8 @@ qed-.
 
 (* Basic_1: uses: ty3_sconv_pc3 *)
 lemma nta_cpcs_bi (h) (a) (G) (L):
-      â\88\80T1,U1. â¦\83G,Lâ¦\84 â\8a¢ T1 :[h,a] U1 â\86\92 â\88\80T2,U2. â¦\83G,Lâ¦\84 ⊢ T2 :[h,a] U2 →
-      â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ U1 ⬌*[h] U2.
+      â\88\80T1,U1. â\9dªG,Lâ\9d« â\8a¢ T1 :[h,a] U1 â\86\92 â\88\80T2,U2. â\9dªG,Lâ\9d« ⊢ T2 :[h,a] U2 →
+      â\9dªG,Lâ\9d« â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ U1 ⬌*[h] U2.
 #h #a #G #L #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
 elim (cpcs_inv_cprs … HT12) -HT12 #T0 #HT10 #HT02
 /3 width=6 by nta_mono, nta_cprs_conf/