update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqus.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqus.ma
@@ -0,0 +1,38 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/s_computation/fqus.ma".
+include "basic_2/rt_computation/fpbs.ma".
+
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
+
+(* Properties with star-iterated structural successor for closures **********)
+
+lemma fqus_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+                 ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
+/3 width=5 by fpbq_fquq, tri_step/
+qed.
+
+lemma fpbs_fqus_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
+                       ∀G2,L2,T2. ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
+/3 width=5 by fpbs_strap1, fpbq_fquq/
+qed-.
+
+lemma fqus_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
+                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+#h #o #G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
+/3 width=5 by fpbs_strap2, fpbq_fquq/
+qed-.