update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
index d145044228a6ce5044dc86ec13d03ab0abf713e9..d39b9411bf92bfd5cfe73e225fdf77893a158377 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
@@ -27,7 +27,7 @@ include "basic_2/rt_transition/cpg.ma".
 
 (* Basic_2A1: includes: cpr *)
 definition cpm (h) (G) (L) (n): relation2 term term ≝
-           λT1,T2. â\88\83â\88\83c. ð\9d\90\91ð\9d\90\93â\9dªn,câ\9d« & â\9dªG,Lâ\9d« ⊢ T1 ⬈[sh_is_next h,rtc_eq_t,c] T2.
+           λT1,T2. â\88\83â\88\83c. ð\9d\90\91ð\9d\90\93â\9d¨n,câ\9d© & â\9d¨G,Lâ\9d© ⊢ T1 ⬈[sh_is_next h,rtc_eq_t,c] T2.
 
 interpretation
   "t-bound context-sensitive parallel rt-transition (term)"
@@ -36,26 +36,26 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma cpm_ess (h) (G) (L):
-      â\88\80s. â\9dªG,Lâ\9d« ⊢ ⋆s ➡[h,1] ⋆(⫯[h]s).
+      â\88\80s. â\9d¨G,Lâ\9d© ⊢ ⋆s ➡[h,1] ⋆(⫯[h]s).
 /3 width=3 by cpg_ess, ex2_intro/ qed.
 
 lemma cpm_delta (h) (n) (G) (K):
-      â\88\80V1,V2,W2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,n] V2 →
-      â\87§[1] V2 â\89\98 W2 â\86\92 â\9dªG,K.â\93\93V1â\9d« ⊢ #0 ➡[h,n] W2.
+      â\88\80V1,V2,W2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,n] V2 →
+      â\87§[1] V2 â\89\98 W2 â\86\92 â\9d¨G,K.â\93\93V1â\9d© ⊢ #0 ➡[h,n] W2.
 #h #n #G #K #V1 #V2 #W2 *
 /3 width=5 by cpg_delta, ex2_intro/
 qed.
 
 lemma cpm_ell (h) (n) (G) (K):
-      â\88\80V1,V2,W2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,n] V2 →
-      â\87§[1] V2 â\89\98 W2 â\86\92 â\9dªG,K.â\93\9bV1â\9d« ⊢ #0 ➡[h,↑n] W2.
+      â\88\80V1,V2,W2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,n] V2 →
+      â\87§[1] V2 â\89\98 W2 â\86\92 â\9d¨G,K.â\93\9bV1â\9d© ⊢ #0 ➡[h,↑n] W2.
 #h #n #G #K #V1 #V2 #W2 *
 /3 width=5 by cpg_ell, ex2_intro, isrt_succ/
 qed.
 
 lemma cpm_lref (h) (n) (G) (K):
-      â\88\80I,T,U,i. â\9dªG,Kâ\9d« ⊢ #i ➡[h,n] T →
-      â\87§[1] T â\89\98 U â\86\92 â\9dªG,K.â\93\98[I]â\9d« ⊢ #↑i ➡[h,n] U.
+      â\88\80I,T,U,i. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,n] T →
+      â\87§[1] T â\89\98 U â\86\92 â\9d¨G,K.â\93\98[I]â\9d© ⊢ #↑i ➡[h,n] U.
 #h #n #G #K #I #T #U #i *
 /3 width=5 by cpg_lref, ex2_intro/
 qed.
@@ -63,45 +63,45 @@ qed.
 (* Basic_2A1: includes: cpr_bind *)
 lemma cpm_bind (h) (n) (G) (L):
       ∀p,I,V1,V2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ➡[h,n] T2 →
-      â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ➡[h,n] ⓑ[p,I]V2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ➡[h,n] T2 →
+      â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ➡[h,n] ⓑ[p,I]V2.T2.
 #h #n #G #L #p #I #V1 #V2 #T1 #T2 * #cV #HcV #HV12 *
 /5 width=5 by cpg_bind, isrt_max_O1, isr_shift, ex2_intro/
 qed.
 
 lemma cpm_appl (h) (n) (G) (L):
       ∀V1,V2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 →
-      â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ➡[h,n] ⓐV2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 →
+      â\9d¨G,Lâ\9d© ⊢ ⓐV1.T1 ➡[h,n] ⓐV2.T2.
 #h #n #G #L #V1 #V2 #T1 #T2 * #cV #HcV #HV12 *
 /5 width=5 by isrt_max_O1, isr_shift, cpg_appl, ex2_intro/
 qed.
 
 lemma cpm_cast (h) (n) (G) (L):
       ∀U1,U2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ U1 â\9e¡[h,n] U2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 →
-      â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ➡[h,n] ⓝU2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ U1 â\9e¡[h,n] U2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 →
+      â\9d¨G,Lâ\9d© ⊢ ⓝU1.T1 ➡[h,n] ⓝU2.T2.
 #h #n #G #L #U1 #U2 #T1 #T2 * #cU #HcU #HU12 *
 /4 width=6 by cpg_cast, isrt_max_idem1, isrt_mono, ex2_intro/
 qed.
 
 (* Basic_2A1: includes: cpr_zeta *)
 lemma cpm_zeta (h) (n) (G) (L):
-      â\88\80T1,T. â\87§[1] T â\89\98 T1 â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T ➡[h,n] T2 →
-      â\88\80V. â\9dªG,Lâ\9d« ⊢ +ⓓV.T1 ➡[h,n] T2.
+      â\88\80T1,T. â\87§[1] T â\89\98 T1 â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T ➡[h,n] T2 →
+      â\88\80V. â\9d¨G,Lâ\9d© ⊢ +ⓓV.T1 ➡[h,n] T2.
 #h #n #G #L #T1 #T #HT1 #T2 *
 /3 width=5 by cpg_zeta, isrt_plus_O2, ex2_intro/
 qed.
 
 (* Basic_2A1: includes: cpr_eps *)
 lemma cpm_eps (h) (n) (G) (L):
-      â\88\80V,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ ⓝV.T1 ➡[h,n] T2.
+      â\88\80V,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡[h,n] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ ⓝV.T1 ➡[h,n] T2.
 #h #n #G #L #V #T1 #T2 *
 /3 width=3 by cpg_eps, isrt_plus_O2, ex2_intro/
 qed.
 
 lemma cpm_ee (h) (n) (G) (L):
-      â\88\80V1,V2,T. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,n] V2 â\86\92 â\9dªG,Lâ\9d« ⊢ ⓝV1.T ➡[h,↑n] V2.
+      â\88\80V1,V2,T. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,n] V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ ⓝV1.T ➡[h,↑n] V2.
 #h #n #G #L #V1 #V2 #T *
 /3 width=3 by cpg_ee, isrt_succ, ex2_intro/
 qed.
@@ -109,8 +109,8 @@ qed.
 (* Basic_2A1: includes: cpr_beta *)
 lemma cpm_beta (h) (n) (G) (L):
       ∀p,V1,V2,W1,W2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡[h,n] T2 →
-      â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓛ[p]W1.T1 ➡[h,n] ⓓ[p]ⓝW2.V2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡[h,n] T2 →
+      â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓛ[p]W1.T1 ➡[h,n] ⓓ[p]ⓝW2.V2.T2.
 #h #n #G #L #p #V1 #V2 #W1 #W2 #T1 #T2 * #riV #rhV #HV12 * #riW #rhW #HW12 *
 /6 width=7 by cpg_beta, isrt_plus_O2, isrt_max, isr_shift, ex2_intro/
 qed.
@@ -118,8 +118,8 @@ qed.
 (* Basic_2A1: includes: cpr_theta *)
 lemma cpm_theta (h) (n) (G) (L):
       ∀p,V1,V,V2,W1,W2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V â\86\92 â\87§[1] V â\89\98 V2 â\86\92 â\9dªG,Lâ\9d« ⊢ W1 ➡[h,0] W2 →
-      â\9dªG,L.â\93\93W1â\9d« â\8a¢ T1 â\9e¡[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓓ[p]W1.T1 ➡[h,n] ⓓ[p]W2.ⓐV2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V â\86\92 â\87§[1] V â\89\98 V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ W1 ➡[h,0] W2 →
+      â\9d¨G,L.â\93\93W1â\9d© â\8a¢ T1 â\9e¡[h,n] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓓ[p]W1.T1 ➡[h,n] ⓓ[p]W2.ⓐV2.T2.
 #h #n #G #L #p #V1 #V #V2 #W1 #W2 #T1 #T2 * #riV #rhV #HV1 #HV2 * #riW #rhW #HW12 *
 /6 width=9 by cpg_theta, isrt_plus_O2, isrt_max, isr_shift, ex2_intro/
 qed.
@@ -135,7 +135,7 @@ lemma cpr_refl (h) (G) (L): reflexive … (cpm h G L 0).
 (* Advanced properties ******************************************************)
 
 lemma cpm_sort (h) (n) (G) (L): n ≤ 1 →
-      â\88\80s. â\9dªG,Lâ\9d« ⊢ ⋆s ➡[h,n] ⋆((next h)^n s).
+      â\88\80s. â\9d¨G,Lâ\9d© ⊢ ⋆s ➡[h,n] ⋆((next h)^n s).
 #h * //
 #n #G #L #H #s <(le_n_O_to_eq n) /2 width=1 by le_S_S_to_le/
 qed.
@@ -143,12 +143,12 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 lemma cpm_inv_atom1 (h) (n) (G) (L):
-      â\88\80J,T2. â\9dªG,Lâ\9d« ⊢ ⓪[J] ➡[h,n] T2 →
+      â\88\80J,T2. â\9d¨G,Lâ\9d© ⊢ ⓪[J] ➡[h,n] T2 →
       ∨∨ ∧∧ T2 = ⓪[J] & n = 0
        | ∃∃s. T2 = ⋆(⫯[h]s) & J = Sort s & n = 1
-       | â\88\83â\88\83K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,n] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓓV1 & J = LRef 0
-       | â\88\83â\88\83m,K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,m] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓛV1 & J = LRef 0 & n = ↑m
-       | â\88\83â\88\83I,K,T,i. â\9dªG,Kâ\9d« ⊢ #i ➡[h,n] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I] & J = LRef (↑i).
+       | â\88\83â\88\83K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,n] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓓV1 & J = LRef 0
+       | â\88\83â\88\83m,K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,m] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓛV1 & J = LRef 0 & n = ↑m
+       | â\88\83â\88\83I,K,T,i. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,n] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I] & J = LRef (↑i).
 #h #n #G #L #J #T2 * #c #Hc #H elim (cpg_inv_atom1 … H) -H *
 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or5_intro0, conj/
 | #s1 #s2 #H1 #H2 #H3 #H4 destruct /4 width=3 by isrt_inv_01, or5_intro1, ex3_intro/
@@ -163,7 +163,7 @@ lemma cpm_inv_atom1 (h) (n) (G) (L):
 qed-.
 
 lemma cpm_inv_sort1 (h) (n) (G) (L):
-      â\88\80T2,s1. â\9dªG,Lâ\9d« ⊢ ⋆s1 ➡[h,n] T2 →
+      â\88\80T2,s1. â\9d¨G,Lâ\9d© ⊢ ⋆s1 ➡[h,n] T2 →
       ∧∧ T2 = ⋆(((next h)^n) s1) & n ≤ 1.
 #h #n #G #L #T2 #s1 * #c #Hc #H
 elim (cpg_inv_sort1 … H) -H *
@@ -176,10 +176,10 @@ elim (cpg_inv_sort1 … H) -H *
 qed-.
 
 lemma cpm_inv_zero1 (h) (n) (G) (L):
-      â\88\80T2. â\9dªG,Lâ\9d« ⊢ #0 ➡[h,n] T2 →
+      â\88\80T2. â\9d¨G,Lâ\9d© ⊢ #0 ➡[h,n] T2 →
       ∨∨ ∧∧ T2 = #0 & n = 0
-       | â\88\83â\88\83K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,n] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓓV1
-       | â\88\83â\88\83m,K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,m] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓛV1 & n = ↑m.
+       | â\88\83â\88\83K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,n] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓓV1
+       | â\88\83â\88\83m,K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,m] V2 & ⇧[1] V2 ≘ T2 & L = K.ⓛV1 & n = ↑m.
 #h #n #G #L #T2 * #c #Hc #H elim (cpg_inv_zero1 … H) -H *
 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or3_intro0, conj/
 | #cV #K #V1 #V2 #HV12 #HVT2 #H1 #H2 destruct
@@ -191,7 +191,7 @@ lemma cpm_inv_zero1 (h) (n) (G) (L):
 qed-.
 
 lemma cpm_inv_zero1_unit (h) (n) (I) (K) (G):
-      â\88\80X2. â\9dªG,K.â\93¤[I]â\9d« ⊢ #0 ➡[h,n] X2 → ∧∧ X2 = #0 & n = 0.
+      â\88\80X2. â\9d¨G,K.â\93¤[I]â\9d© ⊢ #0 ➡[h,n] X2 → ∧∧ X2 = #0 & n = 0.
 #h #n #I #G #K #X2 #H
 elim (cpm_inv_zero1 … H) -H *
 [ #H1 #H2 destruct /2 width=1 by conj/
@@ -201,9 +201,9 @@ elim (cpm_inv_zero1 … H) -H *
 qed.
 
 lemma cpm_inv_lref1 (h) (n) (G) (L):
-      â\88\80T2,i. â\9dªG,Lâ\9d« ⊢ #↑i ➡[h,n] T2 →
+      â\88\80T2,i. â\9d¨G,Lâ\9d© ⊢ #↑i ➡[h,n] T2 →
       ∨∨ ∧∧ T2 = #(↑i) & n = 0
-       | â\88\83â\88\83I,K,T. â\9dªG,Kâ\9d« ⊢ #i ➡[h,n] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I].
+       | â\88\83â\88\83I,K,T. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,n] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I].
 #h #n #G #L #T2 #i * #c #Hc #H elim (cpg_inv_lref1 … H) -H *
 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or_introl, conj/
 | #I #K #V2 #HV2 #HVT2 #H destruct
@@ -212,7 +212,7 @@ lemma cpm_inv_lref1 (h) (n) (G) (L):
 qed-.
 
 lemma cpm_inv_lref1_ctop (h) (n) (G):
-      â\88\80X2,i. â\9dªG,â\8b\86â\9d« ⊢ #i ➡[h,n] X2 → ∧∧ X2 = #i & n = 0.
+      â\88\80X2,i. â\9d¨G,â\8b\86â\9d© ⊢ #i ➡[h,n] X2 → ∧∧ X2 = #i & n = 0.
 #h #n #G #X2 * [| #i ] #H
 [ elim (cpm_inv_zero1 … H) -H *
   [ #H1 #H2 destruct /2 width=1 by conj/
@@ -227,16 +227,16 @@ lemma cpm_inv_lref1_ctop (h) (n) (G):
 qed.
 
 lemma cpm_inv_gref1 (h) (n) (G) (L):
-      â\88\80T2,l. â\9dªG,Lâ\9d« ⊢ §l ➡[h,n] T2 → ∧∧ T2 = §l & n = 0.
+      â\88\80T2,l. â\9d¨G,Lâ\9d© ⊢ §l ➡[h,n] T2 → ∧∧ T2 = §l & n = 0.
 #h #n #G #L #T2 #l * #c #Hc #H elim (cpg_inv_gref1 … H) -H
 #H1 #H2 destruct /3 width=1 by isrt_inv_00, conj/
 qed-.
 
 (* Basic_2A1: includes: cpr_inv_bind1 *)
 lemma cpm_inv_bind1 (h) (n) (G) (L):
-      â\88\80p,I,V1,T1,U2. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ➡[h,n] U2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ➡[h,n] T2 & U2 = ⓑ[p,I]V2.T2
-       | â\88\83â\88\83T. â\87§[1] T â\89\98 T1 & â\9dªG,Lâ\9d« ⊢ T ➡[h,n] U2 & p = true & I = Abbr.
+      â\88\80p,I,V1,T1,U2. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ➡[h,n] U2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ➡[h,n] T2 & U2 = ⓑ[p,I]V2.T2
+       | â\88\83â\88\83T. â\87§[1] T â\89\98 T1 & â\9d¨G,Lâ\9d© ⊢ T ➡[h,n] U2 & p = true & I = Abbr.
 #h #n #G #L #p #I #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_bind1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
   elim (isrt_inv_max … Hc) -Hc #nV #nT #HcV #HcT #H destruct
@@ -250,9 +250,9 @@ qed-.
 (* Basic_1: includes: pr0_gen_abbr pr2_gen_abbr *)
 (* Basic_2A1: includes: cpr_inv_abbr1 *)
 lemma cpm_inv_abbr1 (h) (n) (G) (L):
-      â\88\80p,V1,T1,U2. â\9dªG,Lâ\9d« ⊢ ⓓ[p]V1.T1 ➡[h,n] U2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,L.â\93\93V1â\9d« ⊢ T1 ➡[h,n] T2 & U2 = ⓓ[p]V2.T2
-       | â\88\83â\88\83T. â\87§[1] T â\89\98 T1 & â\9dªG,Lâ\9d« ⊢ T ➡[h,n] U2 & p = true.
+      â\88\80p,V1,T1,U2. â\9d¨G,Lâ\9d© ⊢ ⓓ[p]V1.T1 ➡[h,n] U2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,L.â\93\93V1â\9d© ⊢ T1 ➡[h,n] T2 & U2 = ⓓ[p]V2.T2
+       | â\88\83â\88\83T. â\87§[1] T â\89\98 T1 & â\9d¨G,Lâ\9d© ⊢ T ➡[h,n] U2 & p = true.
 #h #n #G #L #p #V1 #T1 #U2 #H
 elim (cpm_inv_bind1 … H) -H
 [ /3 width=1 by or_introl/
@@ -263,8 +263,8 @@ qed-.
 (* Basic_1: includes: pr0_gen_abst pr2_gen_abst *)
 (* Basic_2A1: includes: cpr_inv_abst1 *)
 lemma cpm_inv_abst1 (h) (n) (G) (L):
-      â\88\80p,V1,T1,U2. â\9dªG,Lâ\9d« ⊢ ⓛ[p]V1.T1 ➡[h,n] U2 →
-      â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,L.â\93\9bV1â\9d« ⊢ T1 ➡[h,n] T2 & U2 = ⓛ[p]V2.T2.
+      â\88\80p,V1,T1,U2. â\9d¨G,Lâ\9d© ⊢ ⓛ[p]V1.T1 ➡[h,n] U2 →
+      â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,L.â\93\9bV1â\9d© ⊢ T1 ➡[h,n] T2 & U2 = ⓛ[p]V2.T2.
 #h #n #G #L #p #V1 #T1 #U2 #H
 elim (cpm_inv_bind1 … H) -H
 [ /3 width=1 by or_introl/
@@ -273,8 +273,8 @@ elim (cpm_inv_bind1 … H) -H
 qed-.
 
 lemma cpm_inv_abst_bi (h) (n) (G) (L):
-      â\88\80p1,p2,V1,V2,T1,T2. â\9dªG,Lâ\9d« ⊢ ⓛ[p1]V1.T1 ➡[h,n] ⓛ[p2]V2.T2 →
-      â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,L.â\93\9bV1â\9d« ⊢ T1 ➡[h,n] T2 & p1 = p2.
+      â\88\80p1,p2,V1,V2,T1,T2. â\9d¨G,Lâ\9d© ⊢ ⓛ[p1]V1.T1 ➡[h,n] ⓛ[p2]V2.T2 →
+      â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,L.â\93\9bV1â\9d© ⊢ T1 ➡[h,n] T2 & p1 = p2.
 #h #n #G #L #p1 #p2 #V1 #V2 #T1 #T2 #H
 elim (cpm_inv_abst1 … H) -H #XV #XT #HV #HT #H destruct
 /2 width=1 by and3_intro/
@@ -283,10 +283,10 @@ qed-.
 (* Basic_1: includes: pr0_gen_appl pr2_gen_appl *)
 (* Basic_2A1: includes: cpr_inv_appl1 *)
 lemma cpm_inv_appl1 (h) (n) (G) (L):
-      â\88\80V1,U1,U2. â\9dªG,Lâ\9d« ⊢ ⓐ V1.U1 ➡[h,n] U2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,Lâ\9d« ⊢ U1 ➡[h,n] T2 & U2 = ⓐV2.T2
-       | â\88\83â\88\83p,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 & â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡[h,n] T2 & U1 = ⓛ[p]W1.T1 & U2 = ⓓ[p]ⓝW2.V2.T2
-       | â\88\83â\88\83p,V,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V & â\87§[1] V â\89\98 V2 & â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 & â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡[h,n] T2 & U1 = ⓓ[p]W1.T1 & U2 = ⓓ[p]W2.ⓐV2.T2.
+      â\88\80V1,U1,U2. â\9d¨G,Lâ\9d© ⊢ ⓐ V1.U1 ➡[h,n] U2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,n] T2 & U2 = ⓐV2.T2
+       | â\88\83â\88\83p,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 & â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡[h,n] T2 & U1 = ⓛ[p]W1.T1 & U2 = ⓓ[p]ⓝW2.V2.T2
+       | â\88\83â\88\83p,V,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V & â\87§[1] V â\89\98 V2 & â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 & â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ➡[h,n] T2 & U1 = ⓓ[p]W1.T1 & U2 = ⓓ[p]W2.ⓐV2.T2.
 #h #n #G #L #V1 #U1 #U2 * #c #Hc #H elim (cpg_inv_appl1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
   elim (isrt_inv_max … Hc) -Hc #nV #nT #HcV #HcT #H destruct
@@ -310,10 +310,10 @@ lemma cpm_inv_appl1 (h) (n) (G) (L):
 qed-.
 
 lemma cpm_inv_cast1 (h) (n) (G) (L):
-      â\88\80V1,U1,U2. â\9dªG,Lâ\9d« ⊢ ⓝV1.U1 ➡[h,n] U2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,n] V2 & â\9dªG,Lâ\9d« ⊢ U1 ➡[h,n] T2 & U2 = ⓝV2.T2
-       | â\9dªG,Lâ\9d« ⊢ U1 ➡[h,n] U2
-       | â\88\83â\88\83m. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,m] U2 & n = ↑m.
+      â\88\80V1,U1,U2. â\9d¨G,Lâ\9d© ⊢ ⓝV1.U1 ➡[h,n] U2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,n] V2 & â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,n] T2 & U2 = ⓝV2.T2
+       | â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,n] U2
+       | â\88\83â\88\83m. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,m] U2 & n = ↑m.
 #h #n #G #L #V1 #U1 #U2 * #c #Hc #H elim (cpg_inv_cast1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #HcVT #H1 #H2 destruct
   elim (isrt_inv_max … Hc) -Hc #nV #nT #HcV #HcT #H destruct
@@ -332,8 +332,8 @@ qed-.
 
 (* Basic_2A1: includes: cpr_fwd_bind1_minus *)
 lemma cpm_fwd_bind1_minus (h) (n) (G) (L):
-      â\88\80I,V1,T1,T. â\9dªG,Lâ\9d« ⊢ -ⓑ[I]V1.T1 ➡[h,n] T → ∀p.
-      â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ➡[h,n] ⓑ[p,I]V2.T2 & T = -ⓑ[I]V2.T2.
+      â\88\80I,V1,T1,T. â\9d¨G,Lâ\9d© ⊢ -ⓑ[I]V1.T1 ➡[h,n] T → ∀p.
+      â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ➡[h,n] ⓑ[p,I]V2.T2 & T = -ⓑ[I]V2.T2.
 #h #n #G #L #I #V1 #T1 #T * #c #Hc #H #p elim (cpg_fwd_bind1_minus … H p) -H
 /3 width=4 by ex2_2_intro, ex2_intro/
 qed-.
@@ -343,32 +343,32 @@ qed-.
 lemma cpm_ind (h) (Q:relation5 …):
       (∀I,G,L. Q 0 G L (⓪[I]) (⓪[I])) →
       (∀G,L,s. Q 1 G L (⋆s) (⋆(⫯[h]s))) →
-      (â\88\80n,G,K,V1,V2,W2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,n] V2 → Q n G K V1 V2 →
+      (â\88\80n,G,K,V1,V2,W2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,n] V2 → Q n G K V1 V2 →
         ⇧[1] V2 ≘ W2 → Q n G (K.ⓓV1) (#0) W2
-      ) â\86\92 (â\88\80n,G,K,V1,V2,W2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,n] V2 → Q n G K V1 V2 →
+      ) â\86\92 (â\88\80n,G,K,V1,V2,W2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,n] V2 → Q n G K V1 V2 →
         ⇧[1] V2 ≘ W2 → Q (↑n) G (K.ⓛV1) (#0) W2
-      ) â\86\92 (â\88\80n,I,G,K,T,U,i. â\9dªG,Kâ\9d« ⊢ #i ➡[h,n] T → Q n G K (#i) T →
+      ) â\86\92 (â\88\80n,I,G,K,T,U,i. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,n] T → Q n G K (#i) T →
         ⇧[1] T ≘ U → Q n G (K.ⓘ[I]) (#↑i) (U)
-      ) â\86\92 (â\88\80n,p,I,G,L,V1,V2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,p,I,G,L,V1,V2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ➡[h,n] T2 →
         Q 0 G L V1 V2 → Q n G (L.ⓑ[I]V1) T1 T2 → Q n G L (ⓑ[p,I]V1.T1) (ⓑ[p,I]V2.T2)
-      ) â\86\92 (â\88\80n,G,L,V1,V2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,G,L,V1,V2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 →
         Q 0 G L V1 V2 → Q n G L T1 T2 → Q n G L (ⓐV1.T1) (ⓐV2.T2)
-      ) â\86\92 (â\88\80n,G,L,V1,V2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,n] V2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,G,L,V1,V2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,n] V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 →
         Q n G L V1 V2 → Q n G L T1 T2 → Q n G L (ⓝV1.T1) (ⓝV2.T2)
-      ) â\86\92 (â\88\80n,G,L,V,T1,T,T2. â\87§[1] T â\89\98 T1 â\86\92 â\9dªG,Lâ\9d« ⊢ T ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,G,L,V,T1,T,T2. â\87§[1] T â\89\98 T1 â\86\92 â\9d¨G,Lâ\9d© ⊢ T ➡[h,n] T2 →
         Q n G L T T2 → Q n G L (+ⓓV.T1) T2
-      ) â\86\92 (â\88\80n,G,L,V,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,G,L,V,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 →
         Q n G L T1 T2 → Q n G L (ⓝV.T1) T2
-      ) â\86\92 (â\88\80n,G,L,V1,V2,T. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,n] V2 →
+      ) â\86\92 (â\88\80n,G,L,V1,V2,T. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,n] V2 →
         Q n G L V1 V2 → Q (↑n) G L (ⓝV1.T) V2
-      ) â\86\92 (â\88\80n,p,G,L,V1,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,p,G,L,V1,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡[h,n] T2 →
         Q 0 G L V1 V2 → Q 0 G L W1 W2 → Q n G (L.ⓛW1) T1 T2 →
         Q n G L (ⓐV1.ⓛ[p]W1.T1) (ⓓ[p]ⓝW2.V2.T2)
-      ) â\86\92 (â\88\80n,p,G,L,V1,V,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡[h,n] T2 →
+      ) â\86\92 (â\88\80n,p,G,L,V1,V,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V â\86\92 â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ➡[h,n] T2 →
         Q 0 G L V1 V → Q 0 G L W1 W2 → Q n G (L.ⓓW1) T1 T2 →
         ⇧[1] V ≘ V2 → Q n G L (ⓐV1.ⓓ[p]W1.T1) (ⓓ[p]W2.ⓐV2.T2)
       ) →
-      â\88\80n,G,L,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,n] T2 → Q n G L T1 T2.
+      â\88\80n,G,L,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,n] T2 → Q n G L T1 T2.
 #h #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #IH8 #IH9 #IH10 #IH11 #IH12 #IH13 #n #G #L #T1 #T2
 * #c #HC #H generalize in match HC; -HC generalize in match n; -n
 elim H -c -G -L -T1 -T2