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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  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/cprs_cnr.ma".
  16 include "basic_2/rt_computation/cprre.ma".
  17 include "basic_2/dynamic/cnv_preserve.ma".
  18
  19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  20
  21 (* Properties with t-bound evaluation on terms ******************************)
  22
  23 lemma cnv_cpmre_trans (h) (a) (n) (G) (L):
  24       ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
  25       ∀T2. ❪G,L❫ ⊢ T1 ➡*[h,n] 𝐍❪T2❫ → ❪G,L❫ ⊢ T2 ![h,a].
  26 #h #a #n #G #L #T1 #HT1 #T2 * #HT12 #_
  27 /2 width=4 by cnv_cpms_trans/
  28 qed-.
  29
  30 lemma cnv_cpmre_cpms_conf (h) (a) (n) (G) (L):
  31       ∀T. ❪G,L❫ ⊢ T ![h,a] → ∀T1. ❪G,L❫ ⊢ T ➡*[n,h] T1 →
  32       ∀T2. ❪G,L❫ ⊢ T ➡*[h,n] 𝐍❪T2❫ → ❪G,L❫ ⊢ T1 ➡*[h] 𝐍❪T2❫.
  33 #h #a #n #G #L #T0 #HT0 #T1 #HT01 #T2 * #HT02 #HT2
  34 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 <minus_n_n #T0 #HT10 #HT20
  35 lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
  36 /2 width=1 by cpmre_intro/
  37 qed-.
  38
  39 (* Main properties with evaluation for t-bound rt-transition on terms *****)
  40
  41 theorem cnv_cpmre_mono (h) (a) (n) (G) (L):
  42         ∀T. ❪G,L❫ ⊢ T ![h,a] → ∀T1. ❪G,L❫ ⊢ T ➡*[h,n] 𝐍❪T1❫ →
  43         ∀T2. ❪G,L❫ ⊢ T ➡*[h,n] 𝐍❪T2❫ → T1 = T2.
  44 #h #a #n #G #L #T0 #HT0 #T1 * #HT01 #HT1 #T2 * #HT02 #HT2
  45 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 <minus_n_n #T0 #HT10 #HT20
  46 /3 width=7 by cprs_inv_cnr_sn, canc_dx_eq/
  47 qed-.