matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/cpms_fpbg.ma".
  16 include "basic_2/dynamic/cnv.ma".
  17
  18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  19
  20 (* Inductive premises for the preservation results **************************)
  21
  22 definition IH_cnv_cpm_trans_lpr (h) (a): relation3 genv lenv term ≝
  23                                 λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
  24                                 ∀n,T2. ❪G,L1❫ ⊢ T1 ➡[h,n] T2 →
  25                                 ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
  26
  27 definition IH_cnv_cpms_trans_lpr (h) (a): relation3 genv lenv term ≝
  28                                  λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
  29                                  ∀n,T2. ❪G,L1❫ ⊢ T1 ➡*[h,n] T2 →
  30                                  ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
  31
  32 definition IH_cnv_cpm_conf_lpr (h) (a): relation3 genv lenv term ≝
  33                                λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
  34                                ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
  35                                ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
  36                                ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
  37
  38 definition IH_cnv_cpms_strip_lpr (h) (a): relation3 genv lenv term ≝
  39                                  λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
  40                                  ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
  41                                  ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
  42                                  ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
  43
  44 definition IH_cnv_cpms_conf_lpr (h) (a): relation3 genv lenv term ≝
  45                                 λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
  46                                 ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡*[h,n2] T2 →
  47                                 ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
  48                                 ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
  49
  50 (* Auxiliary properties for preservation ************************************)
  51
  52 fact cnv_cpms_trans_lpr_sub (h) (a):
  53      ∀G0,L0,T0.
  54      (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
  55      ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_trans_lpr h a G1 L1 T1.
  56 #h #a #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
  57 @(cpms_ind_dx … H) -n -T2
  58 /3 width=7 by fpbg_cpms_trans/
  59 qed-.
  60
  61 fact cnv_cpm_conf_lpr_sub (h) (a):
  62      ∀G0,L0,T0.
  63      (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
  64      ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
  65 /3 width=8 by cpm_cpms/ qed-.
  66
  67 fact cnv_cpms_strip_lpr_sub (h) (a):
  68      ∀G0,L0,T0.
  69      (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
  70      ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_strip_lpr h a G1 L1 T1.
  71 /3 width=8 by cpm_cpms/ qed-.