∀G,L. ∃k. NF … (RR G L) RS (⋆k).
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.
+ ∀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 CP2s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
- ∀G,L0,L,des. ⇩*[des] L0 ≡ L →
+ ∀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.
(* 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
+#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.