(* *)
(**************************************************************************)
-include "basic_2/syntax/tdeq_tdeq.ma".
-include "basic_2/rt_transition/lfpx_lfdeq.ma".
+include "basic_2/rt_transition/rpx_reqx.ma".
include "basic_2/rt_transition/cnx.ma".
-(* NORMAL TERMS FOR UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ******)
+(* NORMAL TERMS FOR EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION *******)
(* Advanced properties ******************************************************)
-lemma cnx_tdeq_trans: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T1⦄ →
- ∀T2. T1 ≛[h, o] T2 → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T2⦄.
-#h #o #G #L #T1 #HT1 #T2 #HT12 #T #HT2
-elim (tdeq_cpx_trans … HT12 … HT2) -HT2 #T0 #HT10 #HT0
-lapply (HT1 … HT10) -HT1 -HT10 /2 width=5 by tdeq_repl/ (**) (* full auto fails *)
+lemma cnx_teqx_trans (G) (L):
+ ∀T1. ❪G,L❫ ⊢ ⬈𝐍 T1 → ∀T2. T1 ≛ T2 → ❪G,L❫ ⊢ ⬈𝐍 T2.
+#G #L #T1 #HT1 #T2 #HT12 #T #HT2
+elim (teqx_cpx_trans … HT12 … HT2) -HT2 #T0 #HT10 #HT0
+lapply (HT1 … HT10) -HT1 -HT10 /2 width=5 by teqx_repl/ (**) (* full auto fails *)
qed-.