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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/multiple/drops.ma".
18 (* GENERIC COMPUTATION PROPERTIES *******************************************)
20 definition candidate: Type[0] ≝ relation3 genv lenv term.
22 definition CP0 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
23 ∀G,L0,L,T,T0,s,d,e. NF … (RR G L) RS T →
24 ⇩[s, d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → NF … (RR G L0) RS T0.
26 definition CP0s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
27 ∀G,L0,L,s,des. ⇩*[s, des] L0 ≡ L →
28 ∀T,T0. ⇧*[des] T ≡ T0 →
29 NF … (RR G L) RS T → NF … (RR G L0) RS T0.
31 definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
32 ∀G,L. ∃k. NF … (RR G L) RS (⋆k).
34 definition CP2 ≝ λRP:candidate.
35 ∀G,L,T,k. RP G L (ⓐ⋆k.T) → RP G L T.
37 (* requirements for generic computation properties *)
38 record gcp (RR:relation4 genv lenv term term) (RS:relation term) (RP:candidate) : Prop ≝
44 (* Basic properties *********************************************************)
46 (* Basic_1: was: nf2_lift1 *)
47 lemma gcp_lifts: ∀RR,RS. CP0 RR RS → CP0s RR RS.
48 #RR #RS #HRR #G #L1 #L2 #s #des #H elim H -L1 -L2 -des
50 <(lifts_inv_nil … H) -H //
51 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2
52 elim (lifts_inv_cons … H) -H /3 width=10 by/