update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
index 3ef5de466273fa4774a2cfdf073373ed2302fd6d..78eadd4087ea672c1c3a87701eefad09b4fa294a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
@@ -24,21 +24,21 @@ include "basic_2/dynamic/cnv_preserve_sub.ma".
 (* Sub diamond propery with t-bound rt-transition for terms *****************)
 
 fact cnv_cpm_conf_lpr_atom_atom_aux (h) (G) (L1) (L2) (I):
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93ª[I] â\9e¡*[h,0] T & â\9dªG,L2â\9d« ⊢ ⓪[I] ➡*[h,0] T.
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93ª[I] â\9e¡*[h,0] T & â\9d¨G,L2â\9d© ⊢ ⓪[I] ➡*[h,0] T.
 /2 width=3 by ex2_intro/ qed-.
 
 fact cnv_cpm_conf_lpr_atom_ess_aux (h) (G) (L1) (L2) (s):
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\8b\86s â\9e¡*[h,1] T & â\9dªG,L2â\9d« ⊢ ⋆(⫯[h]s) ➡*[h,0] T.
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\8b\86s â\9e¡*[h,1] T & â\9d¨G,L2â\9d© ⊢ ⋆(⫯[h]s) ➡*[h,0] T.
 /3 width=3 by cpm_cpms, ex2_intro/ qed-.
 
 fact cnv_cpm_conf_lpr_atom_delta_aux (h) (a) (G) (L) (i):
-     (â\88\80G0,L0,T0. â\9dªG,L,#iâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d«⊢#i![h,a] →
+     (â\88\80G0,L0,T0. â\9d¨G,L,#iâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d©⊢#i![h,a] →
      ∀K,V. ⇩[i]L ≘ K.ⓓV →
-     â\88\80n,XV. â\9dªG,Kâ\9d« ⊢ V ➡[h,n] XV →
+     â\88\80n,XV. â\9d¨G,Kâ\9d© ⊢ V ➡[h,n] XV →
      ∀X. ⇧[↑i]XV ≘ X →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ #i â\9e¡*[h,n] T & â\9dªG,L2â\9d« ⊢ X ➡*[h,0] T.
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ #i â\9e¡*[h,n] T & â\9d¨G,L2â\9d© ⊢ X ➡*[h,0] T.
 #h #a #G #L #i #IH #HT #K #V #HLK #n #XV #HVX #X #HXV #L1 #HL1 #L2 #HL2
 lapply (cnv_inv_lref_pair … HT … HLK) -HT #HV
 elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1
@@ -54,13 +54,13 @@ elim (cpms_lifts_sn … HVX … HLK2 … HXV) -XV -HLK2 #XV #HVX #HXV
 qed-.
 
 fact cnv_cpm_conf_lpr_atom_ell_aux (h) (a) (G) (L) (i):
-     (â\88\80G0,L0,T0. â\9dªG,L,#iâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d«⊢#i![h,a] →
+     (â\88\80G0,L0,T0. â\9d¨G,L,#iâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d©⊢#i![h,a] →
      ∀K,W. ⇩[i]L ≘ K.ⓛW →
-     â\88\80n,XW. â\9dªG,Kâ\9d« ⊢ W ➡[h,n] XW →
+     â\88\80n,XW. â\9d¨G,Kâ\9d© ⊢ W ➡[h,n] XW →
      ∀X. ⇧[↑i]XW ≘ X →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ #i â\9e¡*[h,â\86\91n] T & â\9dªG,L2â\9d« ⊢ X ➡*[h,0] T.
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ #i â\9e¡*[h,â\86\91n] T & â\9d¨G,L2â\9d© ⊢ X ➡*[h,0] T.
 #h #a #G #L #i #IH #HT #K #W #HLK #n #XW #HWX #X #HXW #L1 #HL1 #L2 #HL2
 lapply (cnv_inv_lref_pair … HT … HLK) -HT #HW
 elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1
@@ -76,13 +76,13 @@ elim (cpms_lifts_sn … HWX … HLK2 … HXW) -XW -HLK2 #XW #HWX #HXW
 qed-.
 
 fact cnv_cpm_conf_lpr_delta_delta_aux (h) (a) (I) (G) (L) (i):
-     (â\88\80G0,L0,T0. â\9dªG,L,#iâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d«⊢#i![h,a] →
+     (â\88\80G0,L0,T0. â\9d¨G,L,#iâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d©⊢#i![h,a] →
      ∀K1,V1. ⇩[i]L ≘ K1.ⓑ[I]V1 → ∀K2,V2. ⇩[i]L ≘ K2.ⓑ[I]V2 →
-     â\88\80n1,XV1. â\9dªG,K1â\9d« â\8a¢ V1 â\9e¡[h,n1] XV1 â\86\92 â\88\80n2,XV2. â\9dªG,K2â\9d« ⊢ V2 ➡[h,n2] XV2 →
+     â\88\80n1,XV1. â\9d¨G,K1â\9d© â\8a¢ V1 â\9e¡[h,n1] XV1 â\86\92 â\88\80n2,XV2. â\9d¨G,K2â\9d© ⊢ V2 ➡[h,n2] XV2 →
      ∀X1. ⇧[↑i]XV1 ≘ X1 → ∀X2. ⇧[↑i]XV2 ≘ X2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ X1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ X2 ➡*[h,n1-n2] T.
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ X1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ X2 ➡*[h,n1-n2] T.
 #h #a #I #G #L #i #IH #HT
 #K #V #HLK #Y #X #HLY #n1 #XV1 #HVX1 #n2 #XV2 #HVX2 #X1 #HXV1 #X2 #HXV2
 #L1 #HL1 #L2 #HL2
@@ -108,12 +108,12 @@ lapply (drops_mono … HLK2 … HLK1) -L -i #H destruct
 qed-.
 
 fact cnv_cpm_conf_lpr_bind_bind_aux (h) (a) (p) (I) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\91[p,I]V.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,0] V2 →
-     â\88\80n1,T1. â\9dªG,L.â\93\91[I]Vâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\91[I]Vâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓑ[p,I]V2.T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\91[p,I]V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,0] V2 →
+     â\88\80n1,T1. â\9d¨G,L.â\93\91[I]Vâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\91[I]Vâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\91[p,I]V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓑ[p,I]V2.T2 ➡*[h,n1-n2] T.
 #h #a #p #I #G0 #L0 #V0 #T0 #IH #H0
 #V1 #HV01 #V2 #HV02 #n1 #T1 #HT01 #n2 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -125,12 +125,12 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 (L1.ⓑ[I]V1) … (L2.ⓑ[I]
 qed-.
 
 fact cnv_cpm_conf_lpr_bind_zeta_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,+â\93\93V.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ +ⓓV.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢V â\9e¡[h,0] V1 â\86\92 â\88\80n1,T1. â\9dªG,L.â\93\93Vâ\9d« ⊢ T ➡[h,n1] T1 →
-     â\88\80T2. â\87§[1]T2 â\89\98 T â\86\92 â\88\80n2,XT2. â\9dªG,Lâ\9d« ⊢ T2 ➡[h,n2] XT2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ +â\93\93V1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ XT2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,+â\93\93V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ +ⓓV.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢V â\9e¡[h,0] V1 â\86\92 â\88\80n1,T1. â\9d¨G,L.â\93\93Vâ\9d© ⊢ T ➡[h,n1] T1 →
+     â\88\80T2. â\87§[1]T2 â\89\98 T â\86\92 â\88\80n2,XT2. â\9d¨G,Lâ\9d© ⊢ T2 ➡[h,n2] XT2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ +â\93\93V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ XT2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #V1 #HV01 #n1 #T1 #HT01 #T2 #HT20 #n2 #XT2 #HXT2
 #L1 #HL01 #L2 #HL02
@@ -145,12 +145,12 @@ elim (cnv_cpm_conf_lpr_sub … IH … HXT12 … HXT2 … HL01 … HL02)
 qed-.
 
 fact cnv_cpm_conf_lpr_zeta_zeta_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,+â\93\93V.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ +ⓓV.T ![h,a] →
+     (â\88\80G0,L0,T0. â\9d¨G,L,+â\93\93V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ +ⓓV.T ![h,a] →
      ∀T1. ⇧[1]T1 ≘ T → ∀T2. ⇧[1]T2 ≘ T →
-     â\88\80n1,XT1. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n1] XT1 â\86\92 â\88\80n2,XT2. â\9dªG,Lâ\9d« ⊢ T2 ➡[h,n2] XT2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ XT1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ XT2 ➡*[h,n1-n2] T.
+     â\88\80n1,XT1. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡[h,n1] XT1 â\86\92 â\88\80n2,XT2. â\9d¨G,Lâ\9d© ⊢ T2 ➡[h,n2] XT2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ XT1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ XT2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #T1 #HT10 #T2 #HT20 #n1 #XT1 #HXT1 #n2 #XT2 #HXT2
 #L1 #HL01 #L2 #HL02
@@ -164,12 +164,12 @@ elim (cnv_cpm_conf_lpr_sub … IH … HXT1 … HXT2 … HL01 … HL02)
 qed-.
 
 fact cnv_cpm_conf_lpr_appl_appl_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓐV.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,0] V2 →
-     â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓐV2.T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\90V.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓐV.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,0] V2 →
+     â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓐV2.T2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #V1 #HV01 #V2 #HV02 #n1 #T1 #HT01 #n2 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -181,13 +181,13 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_appl_beta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\9b[p]W.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓐV.ⓛ[p]W.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,0] V2 →
-     â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h,0] W2 →
-     â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ â\93\9b[p]W.T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\9bWâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓓ[p]ⓝW2.V2.T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\90V.â\93\9b[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓐV.ⓛ[p]W.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,0] V2 →
+     â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W ➡[h,0] W2 →
+     â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ â\93\9b[p]W.T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\9bWâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓓ[p]ⓝW2.V2.T2 ➡*[h,n1-n2] T.
 #h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
 #V1 #HV01 #V2 #HV02 #W2 #HW02 #n1 #X #HX #n2 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -203,14 +203,14 @@ lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 [ /2 width=1 by lsubr_
 qed-.
 
 fact cnv_cpm_conf_lpr_appl_theta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\93[p]W.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓐV.ⓓ[p]W.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,0] V2 →
-     â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h,0] W2 →
-     â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ â\93\93[p]W.T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\93Wâ\9d« ⊢ T ➡[h,n2] T2 →
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\90V.â\93\93[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓐV.ⓓ[p]W.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,0] V2 →
+     â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W ➡[h,0] W2 →
+     â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ â\93\93[p]W.T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\93Wâ\9d© ⊢ T ➡[h,n2] T2 →
      ∀U2. ⇧[1]V2 ≘ U2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓓ[p]W2.ⓐU2.T2 ➡*[h,n1-n2] T.
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓓ[p]W2.ⓐU2.T2 ➡*[h,n1-n2] T.
 #h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
 #V1 #HV01 #V2 #HV02 #W2 #HW02 #n1 #X #HX #n2 #T2 #HT02 #U2 #HVU2
 #L1 #HL01 #L2 #HL02
@@ -234,13 +234,13 @@ elim (cpm_inv_abbr1 … HX) -HX *
 qed-.
 
 fact cnv_cpm_conf_lpr_beta_beta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\9b[p]W.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓐV.ⓛ[p]W.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,0] V2 →
-     â\88\80W1. â\9dªG,Lâ\9d« â\8a¢ W â\9e¡[h,0] W1 â\86\92 â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h,0] W2 →
-     â\88\80n1,T1. â\9dªG,L.â\93\9bWâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\9bWâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\93[p]â\93\9dW1.V1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓓ[p]ⓝW2.V2.T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\90V.â\93\9b[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓐV.ⓛ[p]W.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,0] V2 →
+     â\88\80W1. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W1 â\86\92 â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W ➡[h,0] W2 →
+     â\88\80n1,T1. â\9d¨G,L.â\93\9bWâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\9bWâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\93[p]â\93\9dW1.V1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓓ[p]ⓝW2.V2.T2 ➡*[h,n1-n2] T.
 #h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
 #V1 #HV01 #V2 #HV02 #W1 #HW01 #W2 #HW02 #n1 #T1 #HT01 #n2 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -256,14 +256,14 @@ lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_be
 qed-.
 
 fact cnv_cpm_conf_lpr_theta_theta_aux (h) (a) (p) (G) (L) (V) (W) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\90V.â\93\93[p]W.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓐV.ⓓ[p]W.T ![h,a] →
-     â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,0] V2 →
-     â\88\80W1. â\9dªG,Lâ\9d« â\8a¢ W â\9e¡[h,0] W1 â\86\92 â\88\80W2. â\9dªG,Lâ\9d« ⊢ W ➡[h,0] W2 →
-     â\88\80n1,T1. â\9dªG,L.â\93\93Wâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,L.â\93\93Wâ\9d« ⊢ T ➡[h,n2] T2 →
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\90V.â\93\93[p]W.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓐV.ⓓ[p]W.T ![h,a] →
+     â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,0] V1 â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,0] V2 →
+     â\88\80W1. â\9d¨G,Lâ\9d© â\8a¢ W â\9e¡[h,0] W1 â\86\92 â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W ➡[h,0] W2 →
+     â\88\80n1,T1. â\9d¨G,L.â\93\93Wâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,L.â\93\93Wâ\9d© ⊢ T ➡[h,n2] T2 →
      ∀U1. ⇧[1]V1 ≘ U1 → ∀U2. ⇧[1]V2 ≘ U2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\93[p]W1.â\93\90U1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓓ[p]W2.ⓐU2.T2 ➡*[h,n1-n2] T.
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\93[p]W1.â\93\90U1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓓ[p]W2.ⓐU2.T2 ➡*[h,n1-n2] T.
 #h #a #p #G0 #L0 #V0 #W0 #T0 #IH #H0
 #V1 #HV01 #V2 #HV02 #W1 #HW01 #W2 #HW02 #n1 #T1 #HT01 #n2 #T2 #HT02 #U1 #HVU1 #U2 #HVU2
 #L1 #HL01 #L2 #HL02
@@ -279,12 +279,12 @@ lapply (cpm_lifts_bi … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2 … HVU) -V2 -V [ /3
 qed-.
 
 fact cnv_cpm_conf_lpr_cast_cast_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓝV.T ![h,a] →
-     â\88\80n1,V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,n2] V2 →
-     â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ ⓝV2.T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓝV.T ![h,a] →
+     â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,n2] V2 →
+     â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ ⓝV2.T2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #n1 #V1 #HV01 #n2 #V2 #HV02 #T1 #HT01 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -296,12 +296,12 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_cast_epsilon_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓝV.T ![h,a] →
-     â\88\80n1,V1. â\9dªG,Lâ\9d« ⊢ V ➡[h,n1] V1 →
-     â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓝV.T ![h,a] →
+     â\88\80n1,V1. â\9d¨G,Lâ\9d© ⊢ V ➡[h,n1] V1 →
+     â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ T2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #n1 #V1 #HV01 #T1 #HT01 #n2 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -312,13 +312,13 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_cast_ee_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓝV.T ![h,a] →
-     â\88\80n1,V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,n2] V2 →
-     â\88\80T1. â\9dªG,Lâ\9d« ⊢ T ➡[h,n1] T1 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡*[h,â\86\91n2-n1] T & â\9dªG,L2â\9d« ⊢ V2 ➡*[h,n1-↑n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓝV.T ![h,a] →
+     â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,n2] V2 →
+     â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T ➡[h,n1] T1 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡*[h,â\86\91n2-n1] T & â\9d¨G,L2â\9d© ⊢ V2 ➡*[h,n1-↑n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH2 #IH1 #H0
 #n1 #V1 #HV01 #n2 #V2 #HV02 #T1 #HT01
 #L1 #HL01 #L2 #HL02 -HV01
@@ -335,11 +335,11 @@ lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
 qed-.
 
 fact cnv_cpm_conf_lpr_epsilon_epsilon_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓝV.T ![h,a] →
-     â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡[h,n2] T2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ T2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓝV.T ![h,a] →
+     â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© ⊢ T ➡[h,n2] T2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ T2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #n1 #T1 #HT01 #n2 #T2 #HT02
 #L1 #HL01 #L2 #HL02
@@ -350,12 +350,12 @@ elim (cnv_cpm_conf_lpr_sub … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 w
 qed-.
 
 fact cnv_cpm_conf_lpr_epsilon_ee_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓝV.T ![h,a] →
-     â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,n2] V2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[h,â\86\91n2-n1] T & â\9dªG,L2â\9d« ⊢ V2 ➡*[h,n1-↑n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓝV.T ![h,a] →
+     â\88\80n1,T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,n1] T1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,n2] V2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡*[h,â\86\91n2-n1] T & â\9d¨G,L2â\9d© ⊢ V2 ➡*[h,n1-↑n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH2 #IH1 #H0
 #n1 #T1 #HT01 #n2 #V2 #HV02
 #L1 #HL01 #L2 #HL02
@@ -372,11 +372,11 @@ lapply (cpms_trans … HT1 … HTU) -T <arith_l2 #H1
 qed-.
 
 fact cnv_cpm_conf_lpr_ee_ee_aux (h) (a) (G) (L) (V) (T):
-     (â\88\80G0,L0,T0. â\9dªG,L,â\93\9dV.Tâ\9d« > â\9dªG0,L0,T0â\9d« → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     â\9dªG,Lâ\9d« ⊢ ⓝV.T ![h,a] →
-     â\88\80n1,V1. â\9dªG,Lâ\9d« â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9dªG,Lâ\9d« ⊢ V ➡[h,n2] V2 →
-     â\88\80L1. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,Lâ\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ V1 â\9e¡*[h,n2-n1] T & â\9dªG,L2â\9d« ⊢ V2 ➡*[h,n1-n2] T.
+     (â\88\80G0,L0,T0. â\9d¨G,L,â\93\9dV.Tâ\9d© > â\9d¨G0,L0,T0â\9d© → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
+     â\9d¨G,Lâ\9d© ⊢ ⓝV.T ![h,a] →
+     â\88\80n1,V1. â\9d¨G,Lâ\9d© â\8a¢ V â\9e¡[h,n1] V1 â\86\92 â\88\80n2,V2. â\9d¨G,Lâ\9d© ⊢ V ➡[h,n2] V2 →
+     â\88\80L1. â\9d¨G,Lâ\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,Lâ\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ V1 â\9e¡*[h,n2-n1] T & â\9d¨G,L2â\9d© ⊢ V2 ➡*[h,n1-n2] T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #n1 #V1 #HV01 #n2 #V2 #HV02
 #L1 #HL01 #L2 #HL02
@@ -388,8 +388,8 @@ qed-.
 
 fact cnv_cpm_conf_lpr_aux (h) (a):
      ∀G0,L0,T0.
-     (â\88\80G1,L1,T1. â\9dªG0,L0,T0â\9d« > â\9dªG1,L1,T1â\9d« → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
-     (â\88\80G1,L1,T1. â\9dªG0,L0,T0â\9d« > â\9dªG1,L1,T1â\9d« → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     (â\88\80G1,L1,T1. â\9d¨G0,L0,T0â\9d© > â\9d¨G1,L1,T1â\9d© → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+     (â\88\80G1,L1,T1. â\9d¨G0,L0,T0â\9d© > â\9d¨G1,L1,T1â\9d© → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
      ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
 #h #a #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
 [ #I #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct