(* *)
(**************************************************************************)
-include "basic_2/rt_transition/lpx_reqx.ma".
+include "static_2/static/reqx_reqx.ma".
+include "basic_2/rt_transition/lpx_reqg.ma".
include "basic_2/rt_computation/rsx.ma".
-(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+(* STRONGLY NORMALIZING REFERRED LOCAL ENVS FOR EXTENDED RT-TRANSITION ******)
(* Advanced properties ******************************************************)
(* Basic_2A1: uses: lsx_lleq_trans *)
-lemma rsx_reqx_trans (h) (G):
- ∀L1,T. G ⊢ ⬈*𝐒[h,T] L1 →
- â\88\80L2. L1 â\89\9b[T] L2 â\86\92 G â\8a¢ â¬\88*ð\9d\90\92[h,T] L2.
-#h #G #L1 #T #H @(rsx_ind … H) -L1
+lemma rsx_reqx_trans (G):
+ ∀L1,T. G ⊢ ⬈*𝐒[T] L1 →
+ â\88\80L2. L1 â\89\85[T] L2 â\86\92 G â\8a¢ â¬\88*ð\9d\90\92[T] L2.
+#G #L1 #T #H @(rsx_ind … H) -L1
#L1 #_ #IHL1 #L2 #HL12 @rsx_intro
-#L #HL2 #HnL2 elim (reqx_lpx_trans … HL2 … HL12) -HL2
-/4 width=5 by reqx_repl/
+#L #HL2 #HnL2 elim (reqg_lpx_trans … HL2 … HL12) -HL2 //
+/4 width=5 by reqg_repl/
qed-.
(* Basic_2A1: uses: lsx_lpx_trans *)
-lemma rsx_lpx_trans (h) (G):
- ∀L1,T. G ⊢ ⬈*𝐒[h,T] L1 →
- ∀L2. ❪G,L1❫ ⊢ ⬈[h] L2 → G ⊢ ⬈*𝐒[h,T] L2.
-#h #G #L1 #T #H @(rsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
-elim (reqx_dec L1 L2 T) /3 width=4 by rsx_reqx_trans/
+lemma rsx_lpx_trans (G):
+ ∀L1,T. G ⊢ ⬈*𝐒[T] L1 →
+ ∀L2. ❪G,L1❫ ⊢ ⬈ L2 → G ⊢ ⬈*𝐒[T] L2.
+#G #L1 #T #H @(rsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
+elim (reqx_dec … L1 L2 T) /3 width=4 by rsx_reqx_trans/
qed-.