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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/grammar/genv.ma".
16 include "basic_2/substitution/ldrops.ma".
18 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
20 definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
21 ∀G,L. ∃k. NF … (RR G L) RS (⋆k).
23 definition CP2 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
24 ∀G,L0,L,T,T0,d,e. NF … (RR G L) RS T →
25 ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → NF … (RR G L0) RS T0.
27 definition CP2s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
28 ∀G,L0,L,des. ⇩*[des] L0 ≡ L →
29 ∀T,T0. ⇧*[des] T ≡ T0 →
30 NF … (RR G L) RS T → NF … (RR G L0) RS T0.
32 definition CP3 ≝ λRP:relation3 genv lenv term.
33 ∀G,L,T,k. RP G L (ⓐ⋆k.T) → RP G L T.
35 definition CP4 ≝ λRP:relation3 genv lenv term.
36 ∀G,L,W,T. RP G L W → RP G L T → RP G L (ⓝW.T).
38 (* requirements for abstract computation properties *)
39 record acp (RR:relation4 genv lenv term term) (RS:relation term) (RP:relation3 genv lenv term) : Prop ≝
46 (* Basic properties *********************************************************)
48 (* Basic_1: was: nf2_lift1 *)
49 lemma acp_lifts: ∀RR,RS. CP2 RR RS → CP2s RR RS.
50 #RR #RS #HRR #G #L1 #L2 #des #H elim H -L1 -L2 -des
52 <(lifts_inv_nil … H) -H //
53 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2
54 elim (lifts_inv_cons … H) -H /3 width=9/