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[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / acp.ma

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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "Basic_2/unfold/ldrops.ma".
-
-(* ABSTRACT COMPUTATION PROPERTIES ******************************************)
-
-definition CP1 ≝ λRR:lenv→relation term. λRS:relation term.
-                 ∀L,k. NF … (RR L) RS (⋆k).
-
-definition CP2 ≝ λRR:lenv→relation term. λRS:relation term.
-                 ∀L,K,W,i. ⇩[0,i] L ≡ K. ⓛW → NF … (RR L) RS (#i).
-
-definition CP3 ≝ λRR:lenv→relation term. λRP:lenv→predicate term.
-                 ∀L,V,k. RP L (ⓐ⋆k.V) → RP L V.
-
-definition CP4 ≝ λRR:lenv→relation term. λRS:relation term.
-                 ∀L0,L,T,T0,d,e. NF … (RR L) RS T → 
-                 ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → NF … (RR L0) RS T0.
-
-definition CP4s ≝ λRR:lenv→relation term. λRS:relation term.
-                  ∀L0,L,des. ⇩*[des] L0 ≡ L →
-                  ∀T,T0. ⇧*[des] T ≡ T0 →
-                  NF … (RR L) RS T → NF … (RR L0) RS T0.
-
-(* requirements for abstract computation properties *)
-record acp (RR:lenv->relation term) (RS:relation term) (RP:lenv→predicate term) : Prop ≝
-{ cp1: CP1 RR RS;
-  cp2: CP2 RR RS;
-  cp3: CP3 RR RP;
-  cp4: CP4 RR RS
-}.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: nf2_lift1 *)
-lemma acp_lifts: ∀RR,RS. CP4 RR RS → CP4s RR RS.
-#RR #RS #HRR #L1 #L2 #des #H elim H -L1 -L2 -des
-[ #L #T1 #T2 #H #HT1
-  <(lifts_inv_nil … H) -H //
-| #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2
-  elim (lifts_inv_cons … H) -H /3 width=9/
-]
-qed.