update in ground static_2 basic_2 apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_equivalence / cpcs_lprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma
index 8d9c5ee409795b9e728b8b340b1f47b4694d7c88..42e2d902b5098bf9a614fd4c480af330dfc961e2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_lprs.ma
@@ -19,20 +19,20 @@ include "basic_2/rt_equivalence/cpcs_cprs.ma".
 
 (* Properties with parallel r-computation for full local environments *******)
 
-lemma lpr_cpcs_trans (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h,0] L2 →
-                              â\88\80T1,T2. â\9dªG,L2â\9d« â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ⬌*[h] T2.
+lemma lpr_cpcs_trans (h) (G): â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] L2 →
+                              â\88\80T1,T2. â\9d¨G,L2â\9d© â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9d¨G,L1â\9d© ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H
  /4 width=5 by cprs_div, lpr_cpms_trans/
 qed-.
 
-lemma lprs_cpcs_trans (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡*[h,0] L2 →
-                               â\88\80T1,T2. â\9dªG,L2â\9d« â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9dªG,L1â\9d« ⊢ T1 ⬌*[h] T2.
+lemma lprs_cpcs_trans (h) (G): â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡*[h,0] L2 →
+                               â\88\80T1,T2. â\9d¨G,L2â\9d© â\8a¢ T1 â¬\8c*[h] T2 â\86\92 â\9d¨G,L1â\9d© ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #H elim (cpcs_inv_cprs … H) -H
 /4 width=5 by cprs_div, lprs_cpms_trans/
 qed-.
 
-lemma lprs_cprs_conf (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡*[h,0] L2 →
-                              â\88\80T1,T2. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[h,0] T2 â\86\92 â\9dªG,L2â\9d« ⊢ T1 ⬌*[h] T2.
+lemma lprs_cprs_conf (h) (G): â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡*[h,0] L2 →
+                              â\88\80T1,T2. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡*[h,0] T2 â\86\92 â\9d¨G,L2â\9d© ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #HT12 elim (lprs_cprs_conf_dx … HT12 … HL12) -L1
 /2 width=3 by cprs_div/
 qed-.
@@ -40,24 +40,24 @@ qed-.
 (* Basic_1: was: pc3_wcpr0_t *)
 (* Basic_1: note: pc3_wcpr0_t should be renamed *)
 (* Note: alternative proof /3 width=5 by lprs_cprs_conf, lpr_lprs/ *)
-lemma lpr_cprs_conf (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h,0] L2 →
-                             â\88\80T1,T2. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[h,0] T2 â\86\92 â\9dªG,L2â\9d« ⊢ T1 ⬌*[h] T2.
+lemma lpr_cprs_conf (h) (G): â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] L2 →
+                             â\88\80T1,T2. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡*[h,0] T2 â\86\92 â\9d¨G,L2â\9d© ⊢ T1 ⬌*[h] T2.
 #h #G #L1 #L2 #HL12 #T1 #T2 #HT12 elim (cprs_lpr_conf_dx … HT12 … HL12) -L1
 /2 width=3 by cprs_div/
 qed-.
 
 (* Basic_1: was only: pc3_pr0_pr2_t *)
 (* Basic_1: note: pc3_pr0_pr2_t should be renamed *)
-lemma lpr_cpr_conf (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h,0] L2 →
-                            â\88\80T1,T2. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡[h,0] T2 â\86\92 â\9dªG,L2â\9d« ⊢ T1 ⬌*[h] T2.
+lemma lpr_cpr_conf (h) (G): â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] L2 →
+                            â\88\80T1,T2. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡[h,0] T2 â\86\92 â\9d¨G,L2â\9d© ⊢ T1 ⬌*[h] T2.
 /3 width=5 by lpr_cprs_conf, cpm_cpms/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
 (* Note: there must be a proof suitable for lfpr *)
 lemma cpcs_inv_abst_bi_sn (h) (G) (L):
-      â\88\80p1,p2,W1,W2,T1,T2. â\9dªG,Lâ\9d« ⊢ ⓛ[p1]W1.T1 ⬌*[h] ⓛ[p2]W2.T2 →
-      â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ W1 â¬\8c*[h] W2 & â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ⬌*[h] T2 & p1 = p2.
+      â\88\80p1,p2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© ⊢ ⓛ[p1]W1.T1 ⬌*[h] ⓛ[p2]W2.T2 →
+      â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ W1 â¬\8c*[h] W2 & â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ⬌*[h] T2 & p1 = p2.
 #h #G #L #p1 #p2 #W1 #W2 #T1 #T2 #H
 elim (cpcs_inv_cprs … H) -H #T #H1 #H2
 elim (cpms_inv_abst_sn … H1) -H1 #W0 #T0 #HW10 #HT10 #H destruct
@@ -68,8 +68,8 @@ lapply (lprs_cpcs_trans … (L.ⓛW1) … HT2) /2 width=1 by lprs_pair/ -HT2 #HT
 qed-.
 
 lemma cpcs_inv_abst_bi_dx (h) (G) (L):
-      â\88\80p1,p2,W1,W2,T1,T2. â\9dªG,Lâ\9d« ⊢ ⓛ[p1]W1.T1 ⬌*[h] ⓛ[p2]W2.T2 →
-      â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ W1 â¬\8c*[h] W2 & â\9dªG,L.â\93\9bW2â\9d« ⊢ T1 ⬌*[h] T2 & p1 = p2.
+      â\88\80p1,p2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© ⊢ ⓛ[p1]W1.T1 ⬌*[h] ⓛ[p2]W2.T2 →
+      â\88§â\88§ â\9d¨G,Lâ\9d© â\8a¢ W1 â¬\8c*[h] W2 & â\9d¨G,L.â\93\9bW2â\9d© ⊢ T1 ⬌*[h] T2 & p1 = p2.
 #h #G #L #p1 #p2 #W1 #W2 #T1 #T2 #HT12 lapply (cpcs_sym … HT12) -HT12
 #HT12 elim (cpcs_inv_abst_bi_sn … HT12) -HT12 /3 width=1 by cpcs_sym, and3_intro/
 qed-.