update in ground static_2 basic_2 apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpr_lpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
index 73509adecf4ba65ec0423b515f9b02987f28cd25..2c94f6c1d6fb9a2a7e2a48569eb482d7bd9543f4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
@@ -21,24 +21,24 @@ include "basic_2/rt_transition/lpr_drops.ma".
 (* PARALLEL R-TRANSITION FOR FULL LOCAL ENVIRONMENTS ************************)
 
 definition IH_cpr_conf_lpr (h): relation3 genv lenv term ≝ λG,L,T.
-                           â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h,0] T1 â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T ➡[h,0] 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\83T0. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡[h,0] T0 & â\9dªG,L2â\9d« ⊢ T2 ➡[h,0] T0.
+                           â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡[h,0] T1 â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T ➡[h,0] 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\83T0. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡[h,0] T0 & â\9d¨G,L2â\9d© ⊢ T2 ➡[h,0] T0.
 
 (* Main properties with context-sensitive parallel reduction for terms ******)
 
 fact cpr_conf_lpr_atom_atom (h):
-   â\88\80I,G,L1,L2. 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\80I,G,L1,L2. 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 cpr_refl, ex2_intro/ qed-.
 
 fact cpr_conf_lpr_atom_delta (h):
    ∀G0,L0,i. (
-      â\88\80G,L,T. â\9dªG0,L0,#iâ\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,#iâ\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
    ∀K0,V0. ⇩[i] L0 ≘ K0.ⓓV0 →
-   â\88\80V2. â\9dªG0,K0â\9d« ⊢ V0 ➡[h,0] V2 → ∀T2. ⇧[↑i] V2 ≘ T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ #i â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ T2 ➡[h,0] T.
+   â\88\80V2. â\9d¨G0,K0â\9d© ⊢ V0 ➡[h,0] V2 → ∀T2. ⇧[↑i] V2 ≘ T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ #i â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ T2 ➡[h,0] T.
 #h #G0 #L0 #i #IH #K0 #V0 #HLK0 #V2 #HV02 #T2 #HVT2 #L1 #HL01 #L2 #HL02
 elim (lpr_drops_conf … HLK0 … HL01) -HL01 // #X1 #H1 #HLK1
 elim (lpr_inv_pair_sn … H1) -H1 #K1 #V1 #HK01 #HV01 #H destruct
@@ -54,14 +54,14 @@ qed-.
 (* Basic_1: includes: pr0_delta_delta pr2_delta_delta *)
 fact cpr_conf_lpr_delta_delta (h):
    ∀G0,L0,i. (
-      â\88\80G,L,T. â\9dªG0,L0,#iâ\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,#iâ\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
    ∀K0,V0. ⇩[i] L0 ≘ K0.ⓓV0 →
-   â\88\80V1. â\9dªG0,K0â\9d« ⊢ V0 ➡[h,0] V1 → ∀T1. ⇧[↑i] V1 ≘ T1 →
+   â\88\80V1. â\9d¨G0,K0â\9d© ⊢ V0 ➡[h,0] V1 → ∀T1. ⇧[↑i] V1 ≘ T1 →
    ∀KX,VX. ⇩[i] L0 ≘ KX.ⓓVX →
-   â\88\80V2. â\9dªG0,KXâ\9d« ⊢ VX ➡[h,0] V2 → ∀T2. ⇧[↑i] V2 ≘ T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ T2 ➡[h,0] T.
+   â\88\80V2. â\9d¨G0,KXâ\9d© ⊢ VX ➡[h,0] V2 → ∀T2. ⇧[↑i] V2 ≘ T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ T2 ➡[h,0] T.
 #h #G0 #L0 #i #IH #K0 #V0 #HLK0 #V1 #HV01 #T1 #HVT1
 #KX #VX #H #V2 #HV02 #T2 #HVT2 #L1 #HL01 #L2 #HL02
 lapply (drops_mono … H … HLK0) -H #H destruct
@@ -79,12 +79,12 @@ qed-.
 
 fact cpr_conf_lpr_bind_bind (h):
    ∀p,I,G0,L0,V0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\91[p,I]V0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\91[p,I]V0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9dªG0,L0.â\93\91[I]V0â\9d« ⊢ T0 ➡[h,0] T1 →
-   â\88\80V2. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80T2. â\9dªG0,L0.â\93\91[I]V0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\91[p,I]V1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ ⓑ[p,I]V2.T2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9d¨G0,L0.â\93\91[I]V0â\9d© ⊢ T0 ➡[h,0] T1 →
+   â\88\80V2. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80T2. â\9d¨G0,L0.â\93\91[I]V0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\91[p,I]V1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ ⓑ[p,I]V2.T2 ➡[h,0] T.
 #h #p #I #G0 #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
 #V2 #HV02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) //
@@ -94,12 +94,12 @@ qed-.
 
 fact cpr_conf_lpr_bind_zeta (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,+â\93\93V0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,+â\93\93V0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9dªG0,L0.â\93\93V0â\9d« ⊢ T0 ➡[h,0] T1 →
-   â\88\80T2. â\87§[1]T2 â\89\98 T0 â\86\92 â\88\80X2. â\9dªG0,L0â\9d« ⊢ T2 ➡[h,0] X2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ +â\93\93V1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ X2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9d¨G0,L0.â\93\93V0â\9d© ⊢ T0 ➡[h,0] T1 →
+   â\88\80T2. â\87§[1]T2 â\89\98 T0 â\86\92 â\88\80X2. â\9d¨G0,L0â\9d© ⊢ T2 ➡[h,0] X2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ +â\93\93V1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ X2 ➡[h,0] T.
 #h #G0 #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
 #T2 #HT20 #X2 #HTX2 #L1 #HL01 #L2 #HL02
 elim (cpm_inv_lifts_sn … HT01 (Ⓣ) … L0 … HT20) -HT01 [| /3 width=1 by drops_refl, drops_drop/ ] #T #HT1 #HT2
@@ -109,12 +109,12 @@ qed-.
 
 fact cpr_conf_lpr_zeta_zeta (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,+â\93\93V0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,+â\93\93V0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80T1. â\87§[1] T1 â\89\98 T0 â\86\92 â\88\80X1. â\9dªG0,L0â\9d« ⊢ T1 ➡[h,0] X1 →
-   â\88\80T2. â\87§[1] T2 â\89\98 T0 â\86\92 â\88\80X2. â\9dªG0,L0â\9d« ⊢ T2 ➡[h,0] X2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ X1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ X2 ➡[h,0] T.
+   â\88\80T1. â\87§[1] T1 â\89\98 T0 â\86\92 â\88\80X1. â\9d¨G0,L0â\9d© ⊢ T1 ➡[h,0] X1 →
+   â\88\80T2. â\87§[1] T2 â\89\98 T0 â\86\92 â\88\80X2. â\9d¨G0,L0â\9d© ⊢ T2 ➡[h,0] X2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ X1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ X2 ➡[h,0] T.
 #h #G0 #L0 #V0 #T0 #IH #T1 #HT10 #X1 #HTX1
 #T2 #HT20 #X2 #HTX2 #L1 #HL01 #L2 #HL02
 lapply (lifts_inj … HT20 … HT10) -HT20 #H destruct
@@ -124,12 +124,12 @@ qed-.
 
 fact cpr_conf_lpr_flat_flat (h):
    ∀I,G0,L0,V0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\95[I]V0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\95[I]V0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,0] T1 →
-   â\88\80V2. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80T2. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\95[I]V1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ ⓕ[I]V2.T2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,0] T1 →
+   â\88\80V2. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\95[I]V1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ ⓕ[I]V2.T2 ➡[h,0] T.
 #h #I #G0 #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
 #V2 #HV02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) //
@@ -139,11 +139,11 @@ qed-.
 
 fact cpr_conf_lpr_flat_eps (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\9dV0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\9dV0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1,T1. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80T2. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ T2 ➡[h,0] T.
+   â\88\80V1,T1. â\9d¨G0,L0â\9d© â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ T2 ➡[h,0] T.
 #h #G0 #L0 #V0 #T0 #IH #V1 #T1 #HT01
 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HT01 … HT02 … HL01 … HL02) // -L0 -V0 -T0
@@ -152,11 +152,11 @@ qed-.
 
 fact cpr_conf_lpr_eps_eps (h):
    ∀G0,L0,V0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\9dV0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\9dV0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80T1. â\9dªG0,L0â\9d« â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80T2. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ T2 ➡[h,0] T.
+   â\88\80T1. â\9d¨G0,L0â\9d© â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ T2 ➡[h,0] T.
 #h #G0 #L0 #V0 #T0 #IH #T1 #HT01
 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HT01 … HT02 … HL01 … HL02) // -L0 -V0 -T0
@@ -165,12 +165,12 @@ qed-.
 
 fact cpr_conf_lpr_flat_beta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\90V0.â\93\9b[p]W0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\90V0.â\93\9b[p]W0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9dªG0,L0â\9d« ⊢ ⓛ[p]W0.T0 ➡[h,0] T1 →
-   â\88\80V2. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80W2. â\9dªG0,L0â\9d« â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9dªG0,L0.â\93\9bW0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ ⓓ[p]ⓝW2.V2.T2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9d¨G0,L0â\9d© ⊢ ⓛ[p]W0.T0 ➡[h,0] T1 →
+   â\88\80V2. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80W2. â\9d¨G0,L0â\9d© â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9d¨G0,L0.â\93\9bW0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ ⓓ[p]ⓝW2.V2.T2 ➡[h,0] T.
 #h #p #G0 #L0 #V0 #W0 #T0 #IH #V1 #HV01 #X #H
 #V2 #HV02 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (cpm_inv_abst1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
@@ -187,13 +187,13 @@ qed-.
 *)
 fact cpr_conf_lpr_flat_theta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\90V0.â\93\93[p]W0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\90V0.â\93\93[p]W0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9dªG0,L0â\9d« ⊢ ⓓ[p]W0.T0 ➡[h,0] T1 →
-   â\88\80V2. â\9dªG0,L0â\9d« ⊢ V0 ➡[h,0] V2 → ∀U2. ⇧[1] V2 ≘ U2 →
-   â\88\80W2. â\9dªG0,L0â\9d« â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9dªG0,L0.â\93\93W0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\90V1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ ⓓ[p]W2.ⓐU2.T2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80T1. â\9d¨G0,L0â\9d© ⊢ ⓓ[p]W0.T0 ➡[h,0] T1 →
+   â\88\80V2. â\9d¨G0,L0â\9d© ⊢ V0 ➡[h,0] V2 → ∀U2. ⇧[1] V2 ≘ U2 →
+   â\88\80W2. â\9d¨G0,L0â\9d© â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9d¨G0,L0.â\93\93W0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\90V1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ ⓓ[p]W2.ⓐU2.T2 ➡[h,0] T.
 #h #p #G0 #L0 #V0 #W0 #T0 #IH #V1 #HV01 #X #H
 #V2 #HV02 #U2 #HVU2 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1 #HV2
@@ -212,12 +212,12 @@ qed-.
 
 fact cpr_conf_lpr_beta_beta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\90V0.â\93\9b[p]W0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\90V0.â\93\9b[p]W0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80W1. â\9dªG0,L0â\9d« â\8a¢ W0 â\9e¡[h,0] W1 â\86\92 â\88\80T1. â\9dªG0,L0.â\93\9bW0â\9d« ⊢ T0 ➡[h,0] T1 →
-   â\88\80V2. â\9dªG0,L0â\9d« â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80W2. â\9dªG0,L0â\9d« â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9dªG0,L0.â\93\9bW0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\93[p]â\93\9dW1.V1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ ⓓ[p]ⓝW2.V2.T2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V1 â\86\92 â\88\80W1. â\9d¨G0,L0â\9d© â\8a¢ W0 â\9e¡[h,0] W1 â\86\92 â\88\80T1. â\9d¨G0,L0.â\93\9bW0â\9d© ⊢ T0 ➡[h,0] T1 →
+   â\88\80V2. â\9d¨G0,L0â\9d© â\8a¢ V0 â\9e¡[h,0] V2 â\86\92 â\88\80W2. â\9d¨G0,L0â\9d© â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9d¨G0,L0.â\93\9bW0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\93[p]â\93\9dW1.V1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ ⓓ[p]ⓝW2.V2.T2 ➡[h,0] T.
 #h #p #G0 #L0 #V0 #W0 #T0 #IH #V1 #HV01 #W1 #HW01 #T1 #HT01
 #V2 #HV02 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1 #HV2
@@ -231,14 +231,14 @@ qed-.
 (* Basic_1: was: pr0_upsilon_upsilon *)
 fact cpr_conf_lpr_theta_theta (h):
    ∀p,G0,L0,V0,W0,T0. (
-      â\88\80G,L,T. â\9dªG0,L0,â\93\90V0.â\93\93[p]W0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cpr_conf_lpr h G L T
+      â\88\80G,L,T. â\9d¨G0,L0,â\93\90V0.â\93\93[p]W0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cpr_conf_lpr h G L T
    ) →
-   â\88\80V1. â\9dªG0,L0â\9d« ⊢ V0 ➡[h,0] V1 → ∀U1. ⇧[1] V1 ≘ U1 →
-   â\88\80W1. â\9dªG0,L0â\9d« â\8a¢ W0 â\9e¡[h,0] W1 â\86\92 â\88\80T1. â\9dªG0,L0.â\93\93W0â\9d« ⊢ T0 ➡[h,0] T1 →
-   â\88\80V2. â\9dªG0,L0â\9d« ⊢ V0 ➡[h,0] V2 → ∀U2. ⇧[1] V2 ≘ U2 →
-   â\88\80W2. â\9dªG0,L0â\9d« â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9dªG0,L0.â\93\93W0â\9d« ⊢ T0 ➡[h,0] T2 →
-   â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-   â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\93[p]W1.â\93\90U1.T1 â\9e¡[h,0] T & â\9dªG0,L2â\9d« ⊢ ⓓ[p]W2.ⓐU2.T2 ➡[h,0] T.
+   â\88\80V1. â\9d¨G0,L0â\9d© ⊢ V0 ➡[h,0] V1 → ∀U1. ⇧[1] V1 ≘ U1 →
+   â\88\80W1. â\9d¨G0,L0â\9d© â\8a¢ W0 â\9e¡[h,0] W1 â\86\92 â\88\80T1. â\9d¨G0,L0.â\93\93W0â\9d© ⊢ T0 ➡[h,0] T1 →
+   â\88\80V2. â\9d¨G0,L0â\9d© ⊢ V0 ➡[h,0] V2 → ∀U2. ⇧[1] V2 ≘ U2 →
+   â\88\80W2. â\9d¨G0,L0â\9d© â\8a¢ W0 â\9e¡[h,0] W2 â\86\92 â\88\80T2. â\9d¨G0,L0.â\93\93W0â\9d© ⊢ T0 ➡[h,0] T2 →
+   â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+   â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\93[p]W1.â\93\90U1.T1 â\9e¡[h,0] T & â\9d¨G0,L2â\9d© ⊢ ⓓ[p]W2.ⓐU2.T2 ➡[h,0] T.
 #h #p #G0 #L0 #V0 #W0 #T0 #IH #V1 #HV01 #U1 #HVU1 #W1 #HW01 #T1 #HT01
 #V2 #HV02 #U2 #HVU2 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1 #HV2
@@ -308,15 +308,15 @@ qed-.
 
 (* Properties with context-sensitive parallel reduction for terms ***********)
 
-lemma lpr_cpr_conf_dx (h) (G): â\88\80L0. â\88\80T0,T1:term. â\9dªG,L0â\9d« â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80L1. â\9dªG,L0â\9d« ⊢ ➡[h,0] L1 →
-                               â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T0 â\9e¡[h,0] T & â\9dªG,L1â\9d« ⊢ T1 ➡[h,0] T.
+lemma lpr_cpr_conf_dx (h) (G): â\88\80L0. â\88\80T0,T1:term. â\9d¨G,L0â\9d© â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80L1. â\9d¨G,L0â\9d© ⊢ ➡[h,0] L1 →
+                               â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T0 â\9e¡[h,0] T & â\9d¨G,L1â\9d© ⊢ T1 ➡[h,0] T.
 #h #G #L0 #T0 #T1 #HT01 #L1 #HL01
 elim (cpr_conf_lpr … HT01 T0 … HL01 … HL01) -HT01 -HL01
 /2 width=3 by ex2_intro/
 qed-.
 
-lemma lpr_cpr_conf_sn (h) (G): â\88\80L0. â\88\80T0,T1:term. â\9dªG,L0â\9d« â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80L1. â\9dªG,L0â\9d« ⊢ ➡[h,0] L1 →
-                               â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T0 â\9e¡[h,0] T & â\9dªG,L0â\9d« ⊢ T1 ➡[h,0] T.
+lemma lpr_cpr_conf_sn (h) (G): â\88\80L0. â\88\80T0,T1:term. â\9d¨G,L0â\9d© â\8a¢ T0 â\9e¡[h,0] T1 â\86\92 â\88\80L1. â\9d¨G,L0â\9d© ⊢ ➡[h,0] L1 →
+                               â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T0 â\9e¡[h,0] T & â\9d¨G,L0â\9d© ⊢ T1 ➡[h,0] T.
 #h #G #L0 #T0 #T1 #HT01 #L1 #HL01
 elim (cpr_conf_lpr … HT01 T0 … L0 … HL01) -HT01 -HL01
 /2 width=3 by ex2_intro/