lemma jsx_csx_conf (h) (G):
∀L1,L2. G ⊢ L1 ⊒[h] L2 →
- ∀T. ❪G,L1❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L2❫ ⊢ ⬈*[h] 𝐒❪T❫.
+ ∀T. ❪G,L1❫ ⊢ ⬈*𝐒[h] T → ❪G,L2❫ ⊢ ⬈*𝐒[h] T.
/3 width=5 by jsx_fwd_lsubr, csx_lsubr_conf/ qed-.
(* Properties with strongly rt-normalizing referred local environments ******)
(* Note: Try by induction on the 2nd premise by generalizing V with f *)
lemma rsx_jsx_trans (h) (G):
- ∀L1,V. G ⊢ ⬈*[h,V] 𝐒❪L1❫ →
- ∀L2. G ⊢ L1 ⊒[h] L2 → G ⊢ ⬈*[h,V] 𝐒❪L2❫.
+ ∀L1,V. G ⊢ ⬈*𝐒[h,V] L1 →
+ ∀L2. G ⊢ L1 ⊒[h] L2 → G ⊢ ⬈*𝐒[h,V] L2.
#h #G #L1 #V @(fqup_wf_ind_eq (Ⓕ) … G L1 V) -G -L1 -V
#G0 #L0 #V0 #IH #G #L1 * *
[ //