include "basic_2/notation/relations/pred_4.ma".
include "basic_2/grammar/genv.ma".
-include "basic_2/relocation/lsubr.ma".
+include "basic_2/static/lsubr.ma".
(* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
cpr G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
| cpr_zeta : ∀G,L,V,T1,T,T2. cpr G (L.ⓓV) T1 T →
⇧[0, 1] T2 ≡ T → cpr G L (+ⓓV.T1) T2
-| cpr_tau : ∀G,L,V,T1,T2. cpr G L T1 T2 → cpr G L (ⓝV.T1) T2
+| cpr_eps : ∀G,L,V,T1,T2. cpr G L T1 T2 → cpr G L (ⓝV.T1) T2
| cpr_beta : ∀a,G,L,V1,V2,W1,W2,T1,T2.
cpr G L V1 V2 → cpr G L W1 W2 → cpr G (L.ⓛW1) T1 T2 →
cpr G L (ⓐV1.ⓛ{a}W1.T1) (ⓓ{a}ⓝW2.V2.T2)
#G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
[ //
| #G #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
- elim (lsubr_fwd_ldrop2_abbr … HL12 … HLK1) -L1 *
+ elim (lsubr_fwd_drop2_abbr … HL12 … HLK1) -L1 *
/3 width=6 by cpr_delta/
|3,7: /4 width=1 by lsubr_bind, cpr_bind, cpr_beta/
-|4,6: /3 width=1 by cpr_flat, cpr_tau/
+|4,6: /3 width=1 by cpr_flat, cpr_eps/
|5,8: /4 width=3 by lsubr_bind, cpr_zeta, cpr_theta/
]
qed-.
elim (lift_split … HVW i i) /3 width=6 by cpr_delta, ex2_2_intro/
| * [ #a ] #I #W1 #U1 #IHW1 #IHU1 #L #d #HLK
elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2
- [ elim (IHU1 (L. ⓑ{I}W1) (d+1)) -IHU1 /3 width=9 by ldrop_drop, cpr_bind, lift_bind, ex2_2_intro/
+ [ elim (IHU1 (L. ⓑ{I}W1) (d+1)) -IHU1 /3 width=9 by drop_drop, cpr_bind, lift_bind, ex2_2_intro/
| elim (IHU1 … HLK) -IHU1 -HLK /3 width=8 by cpr_flat, lift_flat, ex2_2_intro/
]
]
pr2_gen_ctail pr2_ctail
*)
(* Basic_1: removed local theorems 4:
- pr0_delta_tau pr0_cong_delta
+ pr0_delta_eps pr0_cong_delta
pr2_free_free pr2_free_delta
*)