include "basic_2/rt_transition/cpx_reqx.ma".
include "basic_2/rt_computation/csx_csx.ma".
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
(* Properties with sort-irrelevant equivalence for local environments *******)
(* Basic_2A1: uses: csx_lleq_conf *)
-lemma csx_reqx_conf: ∀h,G,L1,T. ❪G,L1❫ ⊢ ⬈*[h] 𝐒❪T❫ →
- ∀L2. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*[h] 𝐒❪T❫.
-#h #G #L1 #T #H
+lemma csx_reqx_conf (G) (L1):
+ ∀T. ❪G,L1❫ ⊢ ⬈*𝐒 T →
+ ∀L2. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T.
+#G #L1 #T #H
@(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
@csx_intro #T2 #HT12 #HnT12
-elim (reqx_cpx_trans … HL12 … HT12) -HT12
-/5 width=5 by cpx_reqx_conf_sn, csx_teqx_trans, teqx_trans/
+lapply (reqx_cpx_trans … HL12 … HT12) -HT12
+/3 width=4 by cpx_reqx_conf_sn/
qed-.
-(* Basic_2A1: uses: csx_lleq_conf *)
-lemma csx_reqx_trans: ∀h,L1,L2,T. L1 ≛[T] L2 →
- ∀G. ❪G,L2❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L1❫ ⊢ ⬈*[h] 𝐒❪T❫.
+(* Basic_2A1: uses: csx_lleq_trans *)
+lemma csx_reqx_trans (G) (L2):
+ ∀L1,T. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒 T → ❪G,L1❫ ⊢ ⬈*𝐒 T.
/3 width=3 by csx_reqx_conf, reqx_sym/ qed-.