matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr_tdeq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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 "static_2/relocation/lifts_tdeq.ma".
  16 include "basic_2/rt_transition/cpr_drops_basic.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL R-TRANSITION FOR TERMS ************************)
  19
  20 (* Properties with context-free sort-irrelevant equivalence *****************)
  21
  22 lemma cpr_abbr_pos (h) (G) (L) (V) (T1):
  23                    ∃∃T2. ⦃G,L⦄ ⊢ +ⓓV.T1 ➡[h] T2 & (+ⓓV.T1 ≛ T2 → ⊥).
  24 #h #G #L #V #U1
  25 elim (cpr_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
  26 elim (tdeq_dec U1 U2) [ -HU12 #HU12 | -HTU2 #HnU12 ]
  27 [ elim (tdeq_inv_lifts_dx … HU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
  28   /3 width=9 by cpm_zeta, tdeq_lifts_inv_pair_sn, ex2_intro/
  29 | @(ex2_intro … (+ⓓV.U2)) [ /2 width=1 by cpm_bind/ ] -HU12 #H
  30   elim (tdeq_inv_pair … H) -H #_ #_ /2 width=1 by/
  31 ]
  32 qed-.