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14
15 include "basic_2/static/lfdeq_lfeq.ma".
16 include "basic_2/rt_transition/lfpx_lpx.ma".
17 include "basic_2/rt_computation/lfsx_lfsx.ma".
18
19 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNBOUND PARALLEL RT-TRANSITION ******)
20
21 (* Properties with unbound rt-transition ************************************)
22
23 lemma lfsx_intro_lpx: ∀h,o,G,L1,T.
24                       (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
25                       G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
26 #h #o #G #L1 #T #HT
27 @lfsx_intro #L2 #H
28 elim (lfpx_inv_lpx_lfeq … H) -H
29 /6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfeq_lfdeq/
30 qed-.
31
32 lemma lfsx_lpx_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
33                       ∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
34 /3 width=3 by lfsx_lfpx_trans, lfpx_lpx/ qed-.
35
36 (* Eliminators with unbound rt-transition ***********************************)
37
38 lemma lfsx_ind_lpx: ∀h,o,G,T. ∀R:predicate lenv.
39                     (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
40                           (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → R L2) →
41                           R L1
42                     ) →
43                     ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄  → R L.
44 /5 width=6 by lfsx_ind, lfpx_lpx/ qed-.