(* GENERIC COMPUTATION PROPERTIES *******************************************)
+definition nf ≝ λRR:relation4 genv lenv term term. λRS:relation term.
+ λG,L,T. NF … (RR G L) RS T.
+
definition candidate: Type[0] ≝ relation3 genv lenv term.
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 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.
+ ∀G. d_liftable1 (nf RR RS G) (Ⓕ).
definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
∀G,L. ∃k. NF … (RR G L) RS (⋆k).
-definition CP2 ≝ λRP:candidate.
+definition CP2 ≝ λRP:candidate. ∀G. d_liftable1 (RP G) (Ⓕ).
+
+definition CP3 ≝ λRP:candidate.
∀G,L,T,k. RP G L (ⓐ⋆k.T) → RP G L T.
(* requirements for generic computation properties *)
record gcp (RR:relation4 genv lenv term term) (RS:relation term) (RP:candidate) : Prop ≝
{ cp0: CP0 RR RS;
cp1: CP1 RR RS;
- cp2: CP2 RP
+ cp2: CP2 RP;
+ cp3: CP3 RP
}.
(* Basic properties *********************************************************)
(* Basic_1: was: nf2_lift1 *)
-lemma gcp_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=10 by/
-]
+lemma gcp0_lifts: ∀RR,RS,RP. gcp RR RS RP → ∀G. d_liftables1 (nf RR RS G) (Ⓕ).
+#RR #RS #RP #H #G @d1_liftable_liftables @(cp0 … H)
+qed.
+
+lemma gcp2_lifts: ∀RR,RS,RP. gcp RR RS RP → ∀G. d_liftables1 (RP G) (Ⓕ).
+#RR #RS #RP #H #G @d1_liftable_liftables @(cp2 … H)
+qed.
+
+(* Basic_1: was only: sns3_lifts1 *)
+lemma gcp2_lifts_all: ∀RR,RS,RP. gcp RR RS RP → ∀G. d_liftables1_all (RP G) (Ⓕ).
+#RR #RS #RP #H #G @d1_liftables_liftables_all /2 width=7 by gcp2_lifts/
qed.