matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lcpr_vector.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/computation/acp_cr.ma".
  16 include "Basic_2/computation/cprs_tstc_vector.ma".
  17 include "Basic_2/computation/csn_lcpr.ma".
  18 include "Basic_2/computation/csn_vector.ma".
  19
  20 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERM VECTORS **********************)
  21
  22 (* Advanced properties ******************************************************)
  23 (*
  24 (* Basic_1: was only: sn3_appl_appls *)
  25 lemma csn_appl_appls_simple_tstc: ∀L,Vs,V,T1. L ⊢ ⬇* V → L ⊢ ⬇* T1 →
  26                                   (∀T2. L ⊢ ⒶVs.T1 ➡* T2 → (ⒶVs.T1 ≃ T2 → False) → L ⊢ ⬇* ⓐV. T2) →
  27                                   𝐒[T1] → L ⊢ ⬇* ⓐV. ⒶVs. T1.
  28 #L *
  29 [ #V #T1 #HV
  30   @csn_appl_simple_tstc //
  31 | #V0 #Vs #V #T1 #HV #H1T1 #H2T1 #H3T1
  32   @csn_appl_simple_tstc // -HV
  33   [ @H2T1
  34 ]
  35 qed.
  36 *)
  37 lemma csn_applv_theta: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
  38                        ∀V,T. L ⊢ ⬇* ⓓV. ⒶV2s. T → L ⊢ ⬇* V → L ⊢ ⬇* ⒶV1s. ⓓV. T.
  39 #L #V1s #V2s * -V1s -V2s /2 width=1/
  40 #V1s #V2s #V1 #V2 #HV12 #H
  41 generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
  42 elim H -V1s -V2s /2 width=3/
  43 #V1s #V2s #V1 #V2 #HV12 #HV12s #IHV12s #W1 #W2 #HW12 #V #T #H #HV
  44 lapply (csn_appl_theta … HW12 … H) -H -HW12 #H
  45 lapply (csn_fwd_pair_sn … H) #HW1
  46 lapply (csn_fwd_flat_dx … H) #H1
  47 @csn_appl_simple_tstc // -HW1 /2 width=3/ -IHV12s -HV -H1 #X #H1 #H2
  48 elim (cprs_fwd_theta_vector … (V2::V2s) … H1) -H1 /2 width=1/ -HV12s -HV12
  49 [ -H #H elim (H2 ?) -H2 //
  50 | -H2 #H1 @(csn_cprs_trans … H) -H /2 width=1/
  51 ]
  52 qed.
  53 (*
  54 theorem csn_acr: acr cpr (eq …) (csn …) (λL,T. L ⊢ ⬇* T).
  55 @mk_acr //
  56 [
  57 |
  58 |
  59 | #L #V1 #V2 #HV12 #V #T #H #HVT
  60   @(csn_applv_theta … HV12) -HV12 //
  61   @(csn_abbr) //
  62 |
  63 | @csn_lift
  64 ]
  65 qed.
  66 *)
  67 axiom csn_acr: acr cpr (eq …) (csn …) (λL,T. L ⊢ ⬇* T).