more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_length.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_length.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/static/rdeq_length.ma".
+include "basic_2/rt_transition/lpx_length.ma".
+include "basic_2/rt_computation/rsx.ma".
+
+(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: lsx_sort *)
+lemma rsx_sort (h) (G): ∀L,s. G ⊢ ⬈*[h,⋆s] 𝐒⦃L⦄.
+#h #G #L1 #s @rsx_intro #L2 #H #Hs
+elim Hs -Hs /3 width=3 by lpx_fwd_length, rdeq_sort_length/
+qed.
+
+(* Basic_2A1: uses: lsx_gref *)
+lemma rsx_gref (h) (G): ∀L,l. G ⊢ ⬈*[h,§l] 𝐒⦃L⦄.
+#h #G #L1 #s @rsx_intro #L2 #H #Hs
+elim Hs -Hs /3 width=3 by lpx_fwd_length, rdeq_gref_length/
+qed.
+
+lemma rsx_unit (h) (G): ∀I,L. G ⊢ ⬈*[h,#0] 𝐒⦃L.ⓤ{I}⦄.
+#h #G #I #L1 @rsx_intro
+#Y #HY #HnY elim HnY -HnY
+elim (lpx_inv_unit_sn … HY) -HY #L2 #HL12 #H destruct
+/3 width=3 by lpx_fwd_length, rdeq_unit_length/
+qed.