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/reduction/cpx_cpys.ma".
  17 include "basic_2/computation/cpxs_cpxs.ma".
  18
  19 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
  20
  21 (* Main properties **********************************************************)
  22
  23 axiom cpys_split_down: ∀G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*×[d, e] T2 →
  24                        ∀i. d ≤ i → i ≤ d + e →
  25                        ∃∃T. ⦃G, L⦄ ⊢ T1 ▶*×[i, d+e-i] T & ⦃G, L⦄ ⊢ T ▶*×[d, i-d] T2.
  26
  27 lemma cpys_tpxs_trans: ∀h,g,G,L,T1,T,d,e. ⦃G, L⦄ ⊢ T1 ▶*×[d, e] T →
  28                        ∀T2. ⦃G, ⋆⦄ ⊢ T ➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
  29 #h #g #G #L #T1 #T #d #e #HT1 #T2 #H @(cpxs_ind … H) -T2
  30 /3 width=5 by cpxs_strap1, cpys_cpx, lsubr_cpx_trans, cpx_cpxs/
  31 qed-.
  32
  33 axiom cpx_fwd_cpys_tpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
  34                          ∃∃T. ⦃G, L⦄ ⊢ T1 ▶*×[0, ∞] T & ⦃G, ⋆⦄ ⊢ T ➡*[h, g] T2.
  35 (*
  36 #h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2
  37 [ /2 width=3 by ex2_intro/
  38 | /4 width=3 by cpx_cpxs, cpx_sort, ex2_intro/
  39 | #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 * #V #HV1 #HV2
  40   elim (lift_total V 0 (i+1)) #W #HVW
  41   lapply (cpxs_lift … HV2 (⋆) (Ⓣ) … HVW … HVW2)
  42   [ @ldrop_atom #H destruct | /3 width=7 by cpys_subst_Y2, ex2_intro/ ]
  43 | #a #I #G #L #V1 #V2 #T1 #T2 #_ #_ * #V #HV1 #HV2 * #T #HT1 #HT2
  44   elim (cpys_split_down … HT1 1) -HT1 // #T0 #HT10 #HT0
  45 (*
  46   @(ex2_intro … (ⓑ{a,I}V.T0))
  47   [ @cpys_bind //
  48   | @(cpxs_bind … HV2) -HV2
  49
  50   /2 width=5 by cpys_tpxs_trans/
  51   ]
  52 *)*)