matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/unfold/sstas_sstas.ma".
  16 include "basic_2/computation/lprs_cprs.ma".
  17 include "basic_2/computation/cpds.ma".
  18
  19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma cpds_cprs_trans: ∀h,g,L,T1,T,T2.
  24                        ⦃h, L⦄ ⊢ T1 •*➡*[g] T → L ⊢ T ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  25 #h #g #L #T1 #T #T2 * #T0 #HT10 #HT0 #HT2
  26 lapply (cprs_trans … HT0 … HT2) -T /2 width=3/
  27 qed-.
  28
  29 lemma sstas_cpds_trans: ∀h,g,L,T1,T,T2.
  30                         ⦃h, L⦄ ⊢ T1 •*[g] T → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  31 #h #g #L #T1 #T #T2 #HT1 * #T0 #HT0 #HT02
  32 lapply (sstas_trans … HT1 … HT0) -T /2 width=3/
  33 qed-.
  34
  35 (* Advanced inversion lemmas ************************************************)
  36
  37 lemma cpds_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1. T1 •*➡*[g] U2 →
  38                       ∃∃V2,T2. L ⊢ V1 ➡* V2 & ⦃h, L.ⓛV1⦄ ⊢ T1 •*➡*[g] T2 &
  39                                U2 = ⓛ{a}V2. T2.
  40 #h #g #a #L #V1 #T1 #U2 * #X #H1 #H2
  41 elim (sstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
  42 elim (cprs_inv_abst1 … H2) -H2 #V2 #T2 #HV12 #HUT2 #H destruct /3 width=5/
  43 qed-.
  44
  45 lemma cpds_inv_abbr_abst: ∀h,g,a1,a2,L,V1,W2,T1,T2. ⦃h, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[g] ⓛ{a2}W2.T2 →
  46                           ∃∃T. ⦃h, L.ⓓV1⦄ ⊢ T1 •*➡*[g] T & ⇧[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
  47 #h #g #a1 #a2 #L #V1 #W2 #T1 #T2 * #X #H1 #H2
  48 elim (sstas_inv_bind1 … H1) -H1 #U1 #HTU1 #H destruct
  49 elim (cprs_inv_abbr1 … H2) -H2 *
  50 [ #V2 #U2 #HV12 #HU12 #H destruct
  51 | /3 width=3/
  52 ]
  53 qed-.