matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpue.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/cpms_cnu.ma".
  16 include "basic_2/rt_computation/cpue.ma".
  17 include "basic_2/dynamic/cnv_preserve.ma".
  18
  19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  20
  21 (* Properties with evaluation for t-unbound rt-transition on terms **********)
  22
  23 lemma cnv_cpue_trans (a) (h) (G) (L):
  24       ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
  25       ∀T2. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
  26 #a #h #G #L #T1 #HT1 #T2 * #n #HT12 #_
  27 /2 width=4 by cnv_cpms_trans/
  28 qed-.
  29
  30 lemma cnv_cpue_cpms_conf (a) (h) (n) (G) (L):
  31       ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T0 ➡*[n,h] T1 →
  32       ∀T2. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T2⦄ →
  33       ∃∃T. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T⦄ & T2 ≅ T.
  34 #a #h #n1 #G #L #T0 #HT0 #T1 #HT01 #T2 * #n2 #HT02 #HT2
  35 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
  36 lapply (cpms_inv_cnu_sn … HT20 HT2) -HT20 #HT20
  37 /4 width=8 by cnu_tueq_trans, ex2_intro/
  38 qed-.
  39
  40 (* Main properties with evaluation for t-unbound rt-transition on terms *****)
  41
  42 theorem cnv_cpue_mono (a) (h) (G) (L):
  43         ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T1⦄ →
  44         ∀T2. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T2⦄ → T1 ≅ T2.
  45 #a #h #G #L #T0 #HT0 #T1 * #n1 #HT01 #HT1 #T2 * #n2 #HT02 #HT2
  46 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
  47 /3 width=8 by cpms_inv_cnu_sn, tueq_canc_dx/
  48 qed-.