matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.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                  *)
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  14
  15 include "static_2/static/lsubr.ma".
  16 include "basic_2/rt_transition/cpg.ma".
  17
  18 (* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
  19
  20 (* Properties with restricted refinement for local environments *************)
  21
  22 lemma lsubr_cpg_trans: ∀Rt,c,h,G. lsub_trans … (cpg Rt h c G) lsubr.
  23 #Rt #c #h #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2
  24 [ //
  25 | /2 width=2 by cpg_ess/
  26 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
  27   elim (lsubr_inv_abbr2 … H) -H #L2 #HL21 #H destruct
  28   /3 width=3 by cpg_delta/
  29 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
  30   elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct
  31   /4 width=3 by cpg_delta, cpg_ell, cpg_ee/
  32 | #c #I1 #G #L1 #T1 #U1 #i #_ #HTU1 #IH #X #H
  33   elim (lsubr_fwd_bind2 … H) -H #I2 #L2 #HL21 #H destruct
  34   /3 width=3 by cpg_lref/
  35 |6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_bind/
  36 |7,8,10,11: /3 width=1 by cpg_appl, cpg_cast, cpg_eps, cpg_ee/
  37 |9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_bind/
  38 ]
  39 qed-.