- more commutations with superclosure: fpb_lfdeq

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / fpb_lfdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_fqus.ma".
+include "basic_2/rt_transition/cpx_lfdeq.ma".
+include "basic_2/rt_transition/lfpx_lfdeq.ma".
+include "basic_2/rt_transition/fpb.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with degree-based equivalence for local environments **********)
+
+(* Basic_2A1: was just: lleq_fpb_trans *)
+lemma lfdeq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≡[h, o, T] K2 →
+                       ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
+                       ∃∃L1,U0. ⦃F, K1, T⦄ ≻[h, o] ⦃G, L1, U0⦄ & U0 ≡[h, o] U & L1 ≡[h, o, U] L2.
+#h #o #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
+[ #G #L2 #U #H2 elim (lfdeq_fqu_trans … H2 … HT) -K2
+  /3 width=5 by fpb_fqu, ex3_2_intro/
+| #U #HTU #HnTU elim (lfdeq_cpx_trans … HT … HTU) -HTU
+  /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf_sn, ex3_2_intro/
+| #L2 #HKL2 #HnKL2 elim (lfdeq_lfpx_trans … HKL2 … HT) -HKL2
+  /6 width=5 by fpb_lfpx, lfdeq_canc_sn, ex3_2_intro/ (* 2 lleq_canc_sn *)
+]
+qed-.