milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
index b9b06348d6a8a49ab7a81739a5f3c0c9d3436405..76ff1a2a1c7d69d12bae7f37c2ef4984b820da6b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/rt_transition/lpr.ma".
 include "basic_2/rt_computation/cpms_fpbg.ma".
 include "basic_2/dynamic/cnv.ma".
 
@@ -20,39 +21,39 @@ include "basic_2/dynamic/cnv.ma".
 (* Inductive premises for the preservation results **************************)
 
 definition IH_cnv_cpm_trans_lpr (h) (a): relation3 genv lenv term ≝
-                                λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
-                                ∀n,T2. ❪G,L1❫ ⊢ T1 ➡[h,n] T2 →
-                                ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
+           λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
+           ∀n,T2. ❪G,L1❫ ⊢ T1 ➡[h,n] T2 →
+           ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
 
 definition IH_cnv_cpms_trans_lpr (h) (a): relation3 genv lenv term ≝
-                                 λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
-                                 ∀n,T2. ❪G,L1❫ ⊢ T1 ➡*[h,n] T2 →
-                                 ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
+           λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
+           ∀n,T2. ❪G,L1❫ ⊢ T1 ➡*[h,n] T2 →
+           ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
 
 definition IH_cnv_cpm_conf_lpr (h) (a): relation3 genv lenv term ≝
-                               λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
-                               ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
-                               ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
-                               ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
+           λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
+           ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
+           ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
+           ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
 
 definition IH_cnv_cpms_strip_lpr (h) (a): relation3 genv lenv term ≝
-                                 λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
-                                 ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
-                                 ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
-                                 ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
+           λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
+           ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
+           ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
+           ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
 
 definition IH_cnv_cpms_conf_lpr (h) (a): relation3 genv lenv term ≝
-                                λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
-                                ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡*[h,n2] T2 →
-                                ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
-                                ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
+           λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
+           ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡*[h,n2] T2 →
+           ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
+           ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
 
 (* Auxiliary properties for preservation ************************************)
 
 fact cnv_cpms_trans_lpr_sub (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
-     ∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpms_trans_lpr h a G1 L1 T1.
+     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_trans_lpr h a G1 L1 T1.
 #h #a #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
 @(cpms_ind_dx … H) -n -T2
 /3 width=7 by fpbg_cpms_trans/
@@ -60,12 +61,12 @@ qed-.
 
 fact cnv_cpm_conf_lpr_sub (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
-     ∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
+     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
 /3 width=8 by cpm_cpms/ qed-.
 
 fact cnv_cpms_strip_lpr_sub (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
-     ∀G1,L1,T1. ❪G0,L0,T0❫ >[h] ❪G1,L1,T1❫ → IH_cnv_cpms_strip_lpr h a G1 L1 T1.
+     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_strip_lpr h a G1 L1 T1.
 /3 width=8 by cpm_cpms/ qed-.