+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/lazysn_6.ma".
-include "basic_2/substitution/lleq.ma".
-include "basic_2/reduction/llpx.ma".
-
-(* LAZY SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS *****************)
-
-definition llsx: ∀h. sd h → relation4 ynat term genv lenv ≝
- λh,g,d,T,G. SN … (llpx h g G d T) (lleq d T).
-
-interpretation
- "lazy extended strong normalization (local environment)"
- 'LazySN h g d T G L = (llsx h g T d G L).
-
-(* Basic eliminators ********************************************************)
-
-lemma llsx_ind: ∀h,g,G,T,d. ∀R:predicate lenv.
- (∀L1. G ⊢ ⋕⬊*[h, g, T, d] L1 →
- (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2 → (L1 ⋕[T, d] L2 → ⊥) → R L2) →
- R L1
- ) →
- ∀L. G ⊢ ⋕⬊*[h, g, T, d] L → R L.
-#h #g #G #T #d #R #H0 #L1 #H elim H -L1
-/5 width=1 by lleq_sym, SN_intro/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma llsx_intro: ∀h,g,G,L1,T,d.
- (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2 → (L1 ⋕[T, d] L2 → ⊥) → G ⊢ ⋕⬊*[h, g, T, d] L2) →
- G ⊢ ⋕⬊*[h, g, T, d] L1.
-/5 width=1 by lleq_sym, SN_intro/ qed.
-
-lemma llsx_sort: ∀h,g,G,L,d,k. G ⊢ ⋕⬊*[h, g, ⋆k, d] L.
-#h #g #G #L1 #d #k @llsx_intro
-#L2 #HL12 #H elim H -H
-/3 width=6 by llpx_fwd_length, lleq_sort/
-qed.
-
-lemma llsx_gref: ∀h,g,G,L,d,p. G ⊢ ⋕⬊*[h, g, §p, d] L.
-#h #g #G #L1 #d #p @llsx_intro
-#L2 #HL12 #H elim H -H
-/3 width=6 by llpx_fwd_length, lleq_gref/
-qed.