matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.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/static/feqg_fqup.ma".
  16 include "static_2/static/feqg_feqg.ma".
  17 include "basic_2/rt_transition/fpb_feqg.ma".
  18 include "basic_2/rt_transition/fpbq.ma".
  19
  20 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
  21
  22 (* Properties with proper parallel rst-transition for closures **************)
  23
  24 lemma fpb_fpbq:
  25       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
  26       ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
  27 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  28 /3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/
  29 qed.
  30
  31 (* Basic_2A1: fpb_fpbq_alt *)
  32 lemma fpb_fpbq_fneqx (S):
  33       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
  34       ∧∧ ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ & (❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥).
  35 /3 width=10 by fpb_fpbq, fpb_inv_feqg, conj/ qed-.
  36
  37 (* Inversrion lemmas with proper parallel rst-transition for closures *******)
  38
  39 (* Basic_2A1: fpbq_inv_fpb_alt *)
  40 lemma fpbq_fneqx_inv_fpb:
  41       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
  42       (❪G1,L1,T1❫ ≅ ❪G2,L2,T2❫ → ⊥) → ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
  43 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  44 [ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ]
  45   [ #H elim H -H /2 width=1 by feqg_refl/
  46   | /2 width=1 by fpb_fqu/
  47   ]
  48 | /4 width=1 by fpb_cpx, teqg_feqg/
  49 | /4 width=1 by fpb_lpx, feqg_intro_sn/
  50 | #G2 #L2 #T2 #H12 #Hn12
  51   elim Hn12 -Hn12 //
  52 ]
  53 qed-.
  54
  55 (* Basic_2A1: uses: fpbq_ind_alt *)
  56 lemma fpbq_inv_fpb:
  57       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
  58       ∨∨ ❪G1,L1,T1❫ ≅ ❪G2,L2,T2❫
  59        | ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
  60 #G1 #G2 #L1 #L2 #T1 #T2 #H
  61 elim (feqg_dec sfull … G1 G2 L1 L2 T1 T2) //
  62 [ /2 width=1 by or_introl/
  63 | /4 width=1 by fpbq_fneqx_inv_fpb, or_intror/
  64 ]
  65 qed-.