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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/unfold/ldrops.ma".
17 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
19 definition CP1 ≝ λRR:lenv→relation term. λRS:relation term.
20 ∀L,k. NF … (RR L) RS (⋆k).
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).
25 definition CP3 ≝ λRR:lenv→relation term. λRP:lenv→predicate term.
26 ∀L,V,k. RP L (ⓐ⋆k.V) → RP L V.
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.
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.
37 (* requirements for abstract computation properties *)
38 record acp (RR:lenv->relation term) (RS:relation term) (RP:lenv→predicate term) : Prop ≝
45 (* Basic properties *********************************************************)
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
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/