(* ABSTRACT COMPUTATION PROPERTIES ******************************************)
-definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
- ∀G,L. ∃k. NF … (RR G L) RS (⋆k).
+definition CP0 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+ ∀G,L0,L,T,T0,s,d,e. NF … (RR G L) RS T →
+ ⇩[s, d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → NF … (RR G L0) RS T0.
-definition CP2 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
- ∀G,L0,L,T,T0,d,e. NF … (RR G L) RS T →
- ⇩[d, e] L0 ≡ L → ⇧[d, e] T ≡ T0 → NF … (RR G L0) RS T0.
-
-definition CP2s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
- ∀G,L0,L,des. ⇩*[des] L0 ≡ L →
+definition CP0s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+ ∀G,L0,L,s,des. ⇩*[s, des] L0 ≡ L →
∀T,T0. ⇧*[des] T ≡ T0 →
NF … (RR G L) RS T → NF … (RR G L0) RS T0.
-definition CP3 ≝ λRP:relation3 genv lenv term.
+definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+ ∀G,L. ∃k. NF … (RR G L) RS (⋆k).
+
+definition CP2 ≝ λRP:relation3 genv lenv term.
∀G,L,T,k. RP G L (ⓐ⋆k.T) → RP G L T.
-definition CP4 ≝ λRP:relation3 genv lenv term.
+definition CP3 ≝ λRP:relation3 genv lenv term.
∀G,L,W,T. RP G L W → RP G L T → RP G L (ⓝW.T).
(* requirements for abstract computation properties *)
record acp (RR:relation4 genv lenv term term) (RS:relation term) (RP:relation3 genv lenv term) : Prop ≝
-{ cp1: CP1 RR RS;
- cp2: CP2 RR RS;
- cp3: CP3 RP;
- cp4: CP4 RP
+{ cp0: CP0 RR RS;
+ cp1: CP1 RR RS;
+ cp2: CP2 RP;
+ cp3: CP3 RP
}.
(* Basic properties *********************************************************)
(* Basic_1: was: nf2_lift1 *)
-lemma acp_lifts: ∀RR,RS. CP2 RR RS → CP2s RR RS.
-#RR #RS #HRR #G #L1 #L2 #des #H elim H -L1 -L2 -des
+lemma acp_lifts: ∀RR,RS. CP0 RR RS → CP0s RR RS.
+#RR #RS #HRR #G #L1 #L2 #s #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/
+ elim (lifts_inv_cons … H) -H /3 width=10 by/
]
qed.