update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma
index dc44cc5b2625408c890080b3bcd333c0934e2f4c..3bb3568f1f6385726f75a529bab972ce8e340230 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma
@@ -22,8 +22,8 @@ include "basic_2/dynamic/cnv_preserve_cpcs.ma".
 (* Forward lemmas with t-bound t-computarion for terms **********************)
 
 lemma cpts_cpms_conf_eq (h) (n) (a) (G) (L):
-      â\88\80T0. â\9dªG,Lâ\9d« â\8a¢ T0 ![h,a] â\86\92 â\88\80T1. â\9dªG,Lâ\9d« ⊢ T0 ⬆*[h,n] T1 →
-      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T0 â\9e¡*[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2.
+      â\88\80T0. â\9d¨G,Lâ\9d© â\8a¢ T0 ![h,a] â\86\92 â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T0 ⬆*[h,n] T1 →
+      â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T0 â\9e¡*[h,n] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ⬌*[h] T2.
 #h #a #n #G #L #T0 #HT0 #T1 #HT01 #T2 #HT02
 /3 width=6 by cpts_fwd_cpms, cnv_cpms_conf_eq/
 qed-.
@@ -31,18 +31,18 @@ qed-.
 (* Inversion lemmas with t-bound t-computarion for terms ********************)
 
 lemma cnv_inv_cast_cpts (h) (a) (nu) (nt) (G) (L):
-      â\88\80U1. â\9dªG,Lâ\9d« â\8a¢ U1 ![h,a] â\86\92 â\88\80U2. â\9dªG,Lâ\9d« ⊢ U1 ⬆*[h,nu] U2 →
-      â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬆*[h,nt] T2 →
-      â\9dªG,Lâ\9d« â\8a¢ U1 â¬\8c*[h,nu,nt] T1 â\86\92 â\9dªG,Lâ\9d« ⊢ U2 ⬌*[h] T2.
+      â\88\80U1. â\9d¨G,Lâ\9d© â\8a¢ U1 ![h,a] â\86\92 â\88\80U2. â\9d¨G,Lâ\9d© ⊢ U1 ⬆*[h,nu] U2 →
+      â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬆*[h,nt] T2 →
+      â\9d¨G,Lâ\9d© â\8a¢ U1 â¬\8c*[h,nu,nt] T1 â\86\92 â\9d¨G,Lâ\9d© ⊢ U2 ⬌*[h] T2.
 #h #a #nu #nt #G #L #U1 #HU1 #U2 #HU12 #T1 #HT1 #T2 #HT12 * #X1 #HUX1 #HTX1
 /3 width=8 by cpts_cpms_conf_eq, cpcs_canc_dx/
 qed-.
 
 lemma cnv_inv_appl_cpts (h) (a) (nv) (nt) (p) (G) (L):
-      â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V1 ![h,a] â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V1 ⬆*[h,nv] V2 →
-      â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬆*[h,nt] T2 →
-      â\88\80V0. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡*[h,nv] V0 â\86\92 â\88\80T0. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,nt] ⓛ[p]V0.T0 →
-      â\88\83â\88\83W0,U0. â\9dªG,Lâ\9d« â\8a¢ V2 â\9e¡*[h,0] W0 & â\9dªG,Lâ\9d« ⊢ T2 ➡*[h,0] ⓛ[p]W0.U0.
+      â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V1 ![h,a] â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬆*[h,nv] V2 →
+      â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬆*[h,nt] T2 →
+      â\88\80V0. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡*[h,nv] V0 â\86\92 â\88\80T0. â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,nt] ⓛ[p]V0.T0 →
+      â\88\83â\88\83W0,U0. â\9d¨G,Lâ\9d© â\8a¢ V2 â\9e¡*[h,0] W0 & â\9d¨G,Lâ\9d© ⊢ T2 ➡*[h,0] ⓛ[p]W0.U0.
 #h #a #nv #nt #p #G #L #V1 #HV1 #V2 #HV12 #T1 #HT1 #T2 #HT12 #V0 #HV20 #T0 #HT20
 lapply (cpts_cpms_conf_eq … HV1 … HV12 … HV20) -nv -V1 #HV20
 lapply (cpts_cpms_conf_eq … HT1 … HT12 … HT20) -nt -T1 #HT20
@@ -56,19 +56,19 @@ qed-.
 (* Properties with t-bound t-computarion for terms **************************)
 
 lemma cnv_cast_cpts (h) (a) (nu) (nt) (G) (L):
-      â\88\80U1. â\9dªG,Lâ\9d« â\8a¢ U1 ![h,a] â\86\92 â\88\80U2. â\9dªG,Lâ\9d« ⊢ U1 ⬆*[h,nu] U2 →
-      â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬆*[h,nt] T2 →
-      â\9dªG,Lâ\9d« â\8a¢ U2 â¬\8c*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ U1 ⬌*[h,nu,nt] T1.
+      â\88\80U1. â\9d¨G,Lâ\9d© â\8a¢ U1 ![h,a] â\86\92 â\88\80U2. â\9d¨G,Lâ\9d© ⊢ U1 ⬆*[h,nu] U2 →
+      â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬆*[h,nt] T2 →
+      â\9d¨G,Lâ\9d© â\8a¢ U2 â¬\8c*[h] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ U1 ⬌*[h,nu,nt] T1.
 #h #a #nu #nt #G #L #U1 #HU1 #U2 #HU12 #T1 #HT1 #T2 #HT12 #HUT2
 elim (cpcs_inv_cprs … HUT2) -HUT2 #X2 #HUX2 #HTX2
 /3 width=5 by cpts_cprs_trans, cpms_div/
 qed-.
 
 lemma cnv_appl_cpts (h) (a) (nv) (nt) (p) (G) (L):
-      â\88\80V1. â\9dªG,Lâ\9d« â\8a¢ V1 ![h,a] â\86\92 â\88\80V2. â\9dªG,Lâ\9d« ⊢ V1 ⬆*[h,nv] V2 →
-      â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬆*[h,nt] T2 →
-      â\88\80V0. â\9dªG,Lâ\9d« â\8a¢ V2 â\9e¡*[h,0] V0 â\86\92 â\88\80T0. â\9dªG,Lâ\9d« ⊢ T2 ➡*[h,0] ⓛ[p]V0.T0 →
-      â\88\83â\88\83W0,U0. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡*[h,nv] W0 & â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,nt] ⓛ[p]W0.U0.
+      â\88\80V1. â\9d¨G,Lâ\9d© â\8a¢ V1 ![h,a] â\86\92 â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬆*[h,nv] V2 →
+      â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T1 ![h,a] â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬆*[h,nt] T2 →
+      â\88\80V0. â\9d¨G,Lâ\9d© â\8a¢ V2 â\9e¡*[h,0] V0 â\86\92 â\88\80T0. â\9d¨G,Lâ\9d© ⊢ T2 ➡*[h,0] ⓛ[p]V0.T0 →
+      â\88\83â\88\83W0,U0. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡*[h,nv] W0 & â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,nt] ⓛ[p]W0.U0.
 #h #a #nv #nt #p #G #L #V1 #HV1 #V2 #HV12 #T1 #HT1 #T2 #HT12 #V0 #HV20 #T0 #HT20
 /3 width=6 by cpts_cprs_trans, ex2_2_intro/
 qed-.