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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "Basic_2/static/aaa.ma".
  16 include "Basic_2/computation/lsubc.ma".
  17
  18 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
  19
  20 (* Main propertis ***********************************************************)
  21
  22 axiom aacr_aaa_csubc: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
  23                         ∀L1,T,A. L1 ⊢ T ÷ A →
  24                         ∀L2. L2 [RP] ⊑ L1 → {L2, T} [RP] ϵ 〚A〛.
  25 (*
  26 #RR #RS #RP #H1RP #H2RP #L1 #T #A #H elim H -L1 -T -A
  27 [ #L #k #L2 #HL2
  28   lapply (aacr_acr … H1RP H2RP 𝕒) #HAtom
  29   @(s2 … HAtom … ◊) // /2 width=2/
  30 | * #L #K #V #B #i #HLK #_ #IHB #L2 #HL2
  31   [
  32   | lapply (aacr_acr … H1RP H2RP B) #HB
  33     @(s2 … HB … ◊) //
  34     @(cp2 … H1RP)
  35 | #L #V #T #B #A #_ #_ #IHB #IHA #L2 #HL2
  36   lapply (aacr_acr … H1RP H2RP A) #HA
  37   lapply (aacr_acr … H1RP H2RP B) #HB
  38   lapply (s1 … HB) -HB #HB
  39   @(s5 … HA … ◊ ◊) // /3 width=1/
  40 | #L #W #T #B #A #_ #_ #IHB #IHA #L2 #HL2
  41   lapply (aacr_acr … H1RP H2RP B) #HB
  42   lapply (s1 … HB) -HB #HB
  43   @(aacr_abst  … H1RP H2RP) /3 width=1/ -HB /4 width=3/
  44 | /3 width=1/
  45 | #L #V #T #A #_ #_ #IH1A #IH2A #L2 #HL2
  46   lapply (aacr_acr … H1RP H2RP A) #HA
  47   lapply (s1 … HA) #H
  48   @(s6 … HA … ◊) /2 width=1/ /3 width=1/
  49 ]
  50 *)
  51 lemma acp_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
  52                ∀L,T,A. L ⊢ T ÷ A → RP L T.
  53 #RR #RS #RP #H1RP #H2RP #L #T #A #HT
  54 lapply (aacr_acr … H1RP H2RP A) #HA
  55 @(s1 … HA) /2 width=4/
  56 qed.