matita/matita/contribs/lambdadelta/basic_2/computation/dxprs_lift.ma

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   3 (*      ||M||                                                             *)
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   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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  14
  15 include "basic_2/unwind/sstas_lift.ma".
  16 include "basic_2/computation/cprs_lift.ma".
  17 include "basic_2/computation/dxprs.ma".
  18
  19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  20
  21 (* Advanced inversion lemmas *************************************************)
  22
  23 lemma dxprs_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1. T1 •*➡*[g] U2 →
  24                        ∃∃V2,T2. L ⊢ V1 ➡* V2 & ⦃h, L.ⓛV1⦄ ⊢ T1 •*➡*[g] T2 &
  25                                 U2 = ⓛ{a}V2. T2.
  26 #h #g #a #L #V1 #T1 #U2 * #X #H1 #H2
  27 elim (sstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
  28 elim (cprs_inv_abst1 Abst V1 … H2) -H2 #V2 #T2 #HV12 #HUT2 #H destruct /3 width=5/
  29 qed-.
  30
  31 (* Advanced properties ******************************************************)
  32
  33 lemma ssta_cprs_dxprs: ∀h,g,L,T1,T,T2,l. ⦃h, L⦄ ⊢ T1 •[g, l+1] T →
  34                        L ⊢ T ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  35 /3 width=3/ qed.
  36
  37 (* Relocation properties ****************************************************)
  38
  39 lemma dxprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
  40                   ∀h,g,T2. ⦃h, K⦄ ⊢ T1 •*➡*[g] T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
  41                   ⦃h, L⦄ ⊢ U1 •*➡*[g] U2.
  42 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #T2 * #T
  43 elim (lift_total T d e) /3 width=11/
  44 qed.
  45
  46 lemma dxprs_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
  47                        ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •*➡*[g] U2 →
  48                        ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •*➡*[g] T2.
  49 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * #U #HU1 #HU2
  50 elim (sstas_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HT1 #HTU
  51 elim (cprs_inv_lift1 … HLK … HTU … HU2) -U -L /3 width=5/
  52 qed-.