update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lfsx_lpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lpxs.ma
new file mode 100644 (file)
index 0000000..8c8bd5a
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lpxs.ma
@@ -0,0 +1,44 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/lfdeq_lfeq.ma".
+include "basic_2/rt_computation/lfpxs_lpxs.ma".
+include "basic_2/rt_computation/lfsx_lfpxs.ma".
+
+(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
+
+(* Properties with uncounted rt-computation *********************************)
+
+lemma lfsx_intro_lpxs: ∀h,o,G,L1,T.
+                       (∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
+                       G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
+#h #o #G #L1 #T #HT
+@lfsx_intro_lfpxs #L2 #H
+elim (lfpxs_inv_lpxs_lfeq … H) -H
+/6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfeq_lfdeq/
+qed-.
+
+lemma lfsx_lpxs_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
+                       ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
+/3 width=3 by lfsx_lfpxs_trans, lfpxs_lpxs/ qed-.
+
+(* Eliminators with uncounted rt-computation ********************************)
+
+lemma lfsx_ind_lpxs: ∀h,o,G,T. ∀R:predicate lenv.
+                     (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
+                           (∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → R L2) →
+                           R L1
+                     ) →
+                     ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄  → R L.
+/5 width=6 by lfsx_ind_lfpxs, lfpxs_lpxs/ qed-.