matita/matita/contribs/lambda_delta/basic_2/computation/acp.ma

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  14
  15 include "basic_2/unfold/ldrops.ma".
  16
  17 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
  18
  19 definition CP1 ≝ λRR:lenv→relation term. λRS:relation term.
  20                  ∀L,k. NF … (RR L) RS (⋆k).
  21
  22 definition CP2 ≝ λRR:lenv→relation term. λRS:relation term.
  23                  ∀L,K,W,i. ⇩[0,i] L ≡ K. ⓛW → NF … (RR L) RS (#i).
  24
  25 definition CP3 ≝ λRR:lenv→relation term. λRP:lenv→predicate term.
  26                  ∀L,V,k. RP L (ⓐ⋆k.V) → RP L V.
  27
  28 definition CP4 ≝ λRR:lenv→relation term. λRS:relation term.
  29                  ∀L0,L,T,T0,d,e. NF … (RR L) RS T →
  30                  ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → NF … (RR L0) RS T0.
  31
  32 definition CP4s ≝ λRR:lenv→relation term. λRS:relation term.
  33                   ∀L0,L,des. ⇩*[des] L0 ≡ L →
  34                   ∀T,T0. ⇧*[des] T ≡ T0 →
  35                   NF … (RR L) RS T → NF … (RR L0) RS T0.
  36
  37 (* requirements for abstract computation properties *)
  38 record acp (RR:lenv->relation term) (RS:relation term) (RP:lenv→predicate term) : Prop ≝
  39 { cp1: CP1 RR RS;
  40   cp2: CP2 RR RS;
  41   cp3: CP3 RR RP;
  42   cp4: CP4 RR RS
  43 }.
  44
  45 (* Basic properties *********************************************************)
  46
  47 (* Basic_1: was: nf2_lift1 *)
  48 lemma acp_lifts: ∀RR,RS. CP4 RR RS → CP4s RR RS.
  49 #RR #RS #HRR #L1 #L2 #des #H elim H -L1 -L2 -des
  50 [ #L #T1 #T2 #H #HT1
  51   <(lifts_inv_nil … H) -H //
  52 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2
  53   elim (lifts_inv_cons … H) -H /3 width=9/
  54 ]
  55 qed.