matita/matita/contribs/lambda_delta/Basic_2/computation/csn_cr.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/computation/acp_cr.ma".
  16 include "Basic_2/computation/csn_lcpr.ma".
  17 include "Basic_2/computation/csn_vector.ma".
  18
  19 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
  20
  21 (* Advanced properties ******************************************************)
  22 (*
  23 lemma csn_applv_theta: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
  24                        ∀V,T. L ⊢ ⬇* ⓓV. ⒶV2s. T → L ⊢ ⬇* V → L ⊢ ⬇* ⒶV1s. ⓓV. T.
  25 #L #V1s #V2s * -V1s -V2s /2 width=1/
  26 #V1s #V2s #V1 #V2 #HV12 * -V1s -V2s /2 width=3/
  27 #V1s #V2s #W1 #W2 #HW12 #HV12s #V #T #H #HV
  28 lapply (csn_appl_theta … HV12 … H) -H -HV12 #H
  29 lapply (csn_fwd_pair_sn … H) #HV1
  30 @csn_appl_simple // #X #H1 #H2
  31 whd in ⊢ (? ? %);
  32 *)
  33 (*
  34 lemma csn_S5: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
  35               ∀V,T. L. ⓓV ⊢ ⬇* ⒶV2s. T → L ⊢ ⬇* V → L ⊢ ⬇* ⒶV1s. ⓓV. T.
  36 #L #V1s #V2s #H elim H -V1s -V2s /2 width=1/
  37 *)
  38
  39 axiom csn_acr: acr cpr (eq …) (csn …) (λL,T. L ⊢ ⬇* T).