include "static_2/static/lsuba_aaa.ma".
include "basic_2/rt_transition/lpx_drops.ma".
-(* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
+(* EXTENDED PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS **************)
(* Properties with atomic arity assignment for terms ************************)
(* Note: lemma 500 *)
(* Basic_2A1: was: cpx_lpx_aaa_conf *)
-lemma cpx_aaa_conf_lpx (h): ∀G,L1,T1,A. ❪G,L1❫ ⊢ T1 ⁝ A →
- ∀T2. ❪G,L1❫ ⊢ T1 ⬈[h] T2 →
- ∀L2. ❪G,L1❫ ⊢ ⬈[h] L2 → ❪G,L2❫ ⊢ T2 ⁝ A.
-#h #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
-[ #G #L1 #s #X #H
- elim (cpx_inv_sort1 … H) -H #H destruct //
+lemma cpx_aaa_conf_lpx (G) (L1):
+ ∀T1,A. ❪G,L1❫ ⊢ T1 ⁝ A →
+ ∀T2. ❪G,L1❫ ⊢ T1 ⬈ T2 →
+ ∀L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L2❫ ⊢ T2 ⁝ A.
+#G #L1 #T1 #A #H elim H -G -L1 -T1 -A
+[ #G #L1 #s1 #X #H
+ elim (cpx_inv_sort1 … H) -H #s2 #H destruct //
| #I #G #K1 #V1 #B #_ #IH #X #HX #Y #HY
elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK12 #HV12 #H destruct
elim (cpx_inv_zero1_pair … HX) -HX
]
qed-.
-lemma cpx_aaa_conf (h): ∀G,L. Conf3 … (aaa G L) (cpx h G L).
+lemma cpx_aaa_conf (G) (L): Conf3 … (aaa G L) (cpx G L).
/2 width=7 by cpx_aaa_conf_lpx/ qed-.
-lemma lpx_aaa_conf (h): ∀G,T. Conf3 … (λL. aaa G L T) (lpx h G).
+lemma lpx_aaa_conf (G):
+ ∀T. Conf3 … (λL. aaa G L T) (lpx G).
/2 width=7 by cpx_aaa_conf_lpx/ qed-.