matita/matita/contribs/lambdadelta/basic_2/etc/cpr/tprs_lift.etc

   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/reducibility/tpr_lift.ma".
  16 include "basic_2/computation/tprs.ma".
  17
  18 (* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
  19
  20 (* Advanced inversion lemmas ************************************************)
  21
  22 lemma tprs_inv_abst1: ∀a,V1,T1,U2. ⓛ{a}V1. T1 ➡* U2 →
  23                       ∃∃V2,T2. V1 ➡* V2 & T1 ➡* T2 & U2 = ⓛ{a}V2. T2.
  24 #a #V1 #T1 #U2 #H @(tprs_ind … H) -U2 /2 width=5/
  25 #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
  26 elim (tpr_inv_abst1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /3 width=5/
  27 qed-.
  28
  29 lemma tprs_inv_abst: ∀a,V1,V2,T1,T2. ⓛ{a}V1. T1 ➡* ⓛ{a}V2. T2 →
  30                      V1 ➡* V2 ∧ T1 ➡* T2.
  31 #a #V1 #V2 #T1 #T2 #H
  32 elim (tprs_inv_abst1 … H) -H #V #T #HV1 #HT1 #H destruct /2 width=1/
  33 qed-.
  34
  35 (* Relocation properties ****************************************************)
  36
  37 (* Note: this was missing in basic_1 *)
  38 lemma tprs_lift: t_liftable tprs.
  39 /3 width=7/ qed.
  40
  41 (* Note: this was missing in basic_1 *)
  42 lemma tprs_inv_lift1: t_deliftable_sn tprs.
  43 /3 width=3 by tpr_inv_lift1, t_deliftable_sn_TC/ qed-.