- advances on lfxs for lfpxs

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma
new file mode 100644 (file)
index 0000000..ce2496b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_fqup.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rt_transition/lfpx_fqup.ma".
+include "basic_2/rt_computation/lfpxs.ma".
+
+(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
+
+(* Advanced eliminators *****************************************************)
+
+(* Basic_2A1: was just: lpxs_ind *)
+lemma lfpxs_ind: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
+                 (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
+                 ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
+#h #G #L1 #T #R #HL1 #IHL1 #L2 #HL12
+@(TC_star_ind … HL1 IHL1 … HL12) //
+qed-.
+
+(* Basic_2A1: was just: lpxs_ind_dx *)
+lemma lfpxs_ind_dx: ∀h,G,L2,T. ∀R:predicate lenv. R L2 →
+                    (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → R L → R L1) →
+                    ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L1.
+#h #o #G #L2 #R #HL2 #IHL2 #L1 #HL12
+@(TC_star_ind_dx … HL2 IHL2 … HL12) //
+qed-.
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: was just: lpxs_refl *)
+lemma lfpxs_refl: ∀h,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, T] L.
+/2 width=1 by lfpx_lfpxs/ qed.