matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_tweq.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 "static_2/syntax/tweq_tweq.ma".
  16 include "static_2/relocation/lifts_tweq.ma".
  17 include "basic_2/rt_transition/cpr_drops_basic.ma".
  18 include "basic_2/rt_computation/cpms.ma".
  19
  20 (* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
  21
  22 (* Properties with sort-irrelevant whd equivalence on terms *****************)
  23
  24 lemma cprs_abbr_pos_twneq (h) (G) (L) (V) (T1):
  25       ∃∃T2. ❪G,L❫ ⊢ +ⓓV.T1 ➡*[h] T2 & (+ⓓV.T1 ≅ T2 → ⊥).
  26 #h #G #L #V #U1
  27 elim (cpr_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
  28 elim (tweq_dec U1 U2) [ #HpU12 | -HTU2 #HnU12 ]
  29 [ @(ex2_intro … T2) (**) (* full auto not tried *)
  30   [ /3 width=6 by cpms_zeta, cpms_step_sn, cpm_bind/
  31   | /4 width=6 by tweq_inv_abbr_pos_x_lifts_y_y, tweq_canc_sn, tweq_abbr_pos/
  32   ]
  33 | /4 width=3 by cpm_cpms, cpm_bind, tweq_inv_abbr_pos_bi, ex2_intro/
  34 ]
  35 qed-.