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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/s_transition/fqu_teqg.ma".
  16 include "static_2/static/feqg.ma".
  17 include "basic_2/rt_transition/fpb_reqg.ma".
  18
  19 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  20
  21 (* Properties with generic equivalence for closures *************************)
  22
  23 (* Basic_2A1: uses: fleq_fpb_trans *)
  24 lemma feqg_fpb_trans (S):
  25       reflexive … S → symmetric … S → Transitive … S →
  26       ∀F1,F2,K1,K2,T1,T2. ❪F1,K1,T1❫ ≛[S] ❪F2,K2,T2❫ →
  27       ∀G2,L2,U2. ❪F2,K2,T2❫ ≻ ❪G2,L2,U2❫ →
  28       ∃∃G1,L1,U1. ❪F1,K1,T1❫ ≻ ❪G1,L1,U1❫ & ❪G1,L1,U1❫ ≛[S] ❪G2,L2,U2❫.
  29 #S #H1S #H2S #H3S #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
  30 #K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
  31 elim (teqg_fpb_trans … HT12 … H12) -T2 // #K0 #T0 #H #HT0 #HK0
  32 elim (reqg_fpb_trans … HK12 … H) -K2 // #L0 #U0 #H #HUT0 #HLK0
  33 @(ex2_3_intro … H) -H (**) (* full auto too slow *)
  34 /4 width=5 by feqg_intro_dx, reqg_trans, teqg_reqg_conf_sn, teqg_trans/
  35 qed-.
  36
  37 (* Inversion lemmas with generic equivalence for closures *******************)
  38
  39 (* Basic_2A1: uses: fpb_inv_fleq *)
  40 lemma fpb_inv_feqg (S):
  41       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
  42       ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥.
  43 #S #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  44 [ #G2 #L2 #T2 #H12 #H elim (feqg_inv_gen_sn … H) -H
  45   /3 width=11 by reqg_fwd_length, fqu_inv_teqg/
  46 | #T2 #_ #HnT #H elim (feqg_inv_gen_sn … H) -H /3 width=2 by teqg_teqx/
  47 | #L2 #_ #HnL #H elim (feqg_inv_gen_sn … H) -H /3 width=2 by reqg_reqx/
  48 ]
  49 qed-.