(**************************************************************************)
include "basic_2/notation/relations/lazysn_5.ma".
-include "basic_2/relocation/lleq.ma".
+include "basic_2/substitution/lleq.ma".
include "basic_2/computation/lpxs.ma".
(* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
lemma lsx_ind: ∀h,g,T,G. ∀R:predicate lenv.
(∀L1. G ⊢ ⋕⬊*[h, g, T] L1 →
- (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[0, T] L2 → ⊥) → R L2) →
+ (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[T, 0] L2 → ⊥) → R L2) →
R L1
) →
∀L. G ⊢ ⋕⬊*[h, g, T] L → R L.
(* Basic properties *********************************************************)
lemma lsx_intro: ∀h,g,T,G,L1.
- (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[0, T] L2 → ⊥) → G ⊢ ⋕⬊*[h, g, T] L2) →
+ (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[T, 0] L2 → ⊥) → G ⊢ ⋕⬊*[h, g, T] L2) →
G ⊢ ⋕⬊*[h, g, T] L1.
/5 width=1 by lleq_sym, SN_intro/ qed.