include "basic_2/rt_transition/lfpx_lpx.ma".
include "basic_2/rt_computation/lfsx_lfsx.ma".
-(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
+(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNBOUND PARALLEL RT-TRANSITION ******)
-(* Properties with uncounted rt-transition **********************************)
+(* Properties with unbound rt-transition ************************************)
lemma lfsx_intro_lpx: ∀h,o,G,L1,T.
(∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
/3 width=3 by lfsx_lfpx_trans, lfpx_lpx/ qed-.
-(* Eliminators with uncounted rt-transition *********************************)
+(* Eliminators with unbound rt-transition ***********************************)
lemma lfsx_ind_lpx: ∀h,o,G,T. ∀R:predicate lenv.
(∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →