matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.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 "basic_2/substitution/cpys_cpys.ma".
  16 include "basic_2/computation/cpxs_cpxs.ma".
  17
  18 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
  19
  20 (* Main properties **********************************************************)
  21
  22 lemma cpx_fwd_cpys_tpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
  23                          ∃∃T. ⦃G, L⦄ ⊢ T1 ▶*×[0, ∞] T & ⦃G, ⋆⦄ ⊢ T ➡*[h, g] T2.
  24 #h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2
  25 [ /2 width=3 by ex2_intro/
  26 | /4 width=3 by cpx_cpxs, cpx_sort, ex2_intro/
  27 | #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 * #V #HV1 #HV2
  28   elim (lift_total V 0 (i+1)) #W #HVW
  29   @(ex2_intro … W) /2 width=7 by cpys_subst_Y2/
  30 | #a #I #G #L #V1 #V2 #T1 #T2 #_ #_ * #V #HV1 #HV2 * #T #HT1 #HT2
  31   elim (cpys_split_up … HT1 1) -HT1 // #T0 #HT10 #HT0
  32   @(ex2_intro … (ⓑ{a,I}V.T0))
  33   [ @(cpys_bind … HV1) -HV1
  34   | @(cpxs_bind … HV2) -HV2
  35   ]