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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/fpbg.ma".
  16 include "basic_2/rt_computation/cpms_fpbs.ma".
  17 include "basic_2/dynamic/cnv.ma".
  18
  19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  20
  21 (* Inductive premises for the preservation results **************************)
  22
  23 definition IH_cnv_cpm_trans_lpr (a) (h): relation3 genv lenv term ≝
  24                                 λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] →
  25                                 ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡[n,h] T2 →
  26                                 ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h].
  27
  28 definition IH_cnv_cpms_trans_lpr (a) (h): relation3 genv lenv term ≝
  29                                  λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] →
  30                                  ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 →
  31                                  ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h].
  32
  33 definition IH_cnv_cpm_conf_lpr (a) (h): relation3 genv lenv term ≝
  34                                λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
  35                                ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 →
  36                                ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
  37                                ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
  38
  39 definition IH_cnv_cpms_strip_lpr (a) (h): relation3 genv lenv term ≝
  40                                  λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
  41                                  ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 →
  42                                  ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
  43                                  ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
  44
  45 definition IH_cnv_cpms_conf_lpr (a) (h): relation3 genv lenv term ≝
  46                                 λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
  47                                 ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h] T2 →
  48                                 ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
  49                                 ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
  50
  51 (* Auxiliary properties for preservation ************************************)
  52
  53 fact cnv_cpms_trans_lpr_sub (a) (h) (o):
  54                             ∀G0,L0,T0.
  55                             (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
  56                             ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_trans_lpr a h G1 L1 T1.
  57 #a #h #o #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
  58 @(cpms_ind_dx … H) -n -T2
  59 /4 width=7 by cpms_fwd_fpbs, fpbg_fpbs_trans/
  60 qed-.
  61
  62 fact cnv_cpm_conf_lpr_sub (a) (h) (o):
  63                           ∀G0,L0,T0.
  64                           (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
  65                           ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_conf_lpr a h G1 L1 T1.
  66 /3 width=8 by cpm_cpms/ qed-.
  67
  68 fact cnv_cpms_strip_lpr_sub (a) (h) (o):
  69                             ∀G0,L0,T0.
  70                             (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
  71                             ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1.
  72 /3 width=8 by cpm_cpms/ qed-.