update for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.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/reqx_fqus.ma".
+include "basic_2/rt_transition/cpx_reqx.ma".
+include "basic_2/rt_transition/lpx_reqx.ma".
+include "basic_2/rt_transition/fpb.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with sort-irrelevant equivalence for local environments *******)
+
+lemma teqx_fpb_trans: ∀h,U2,U1. U2 ≛ U1 →
+                      ∀G1,G2,L1,L2,T1. ⦃G1,L1,U1⦄ ≻[h] ⦃G2,L2,T1⦄ → 
+                      ∃∃L,T2. ⦃G1,L1,U2⦄ ≻[h] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
+#h #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
+[ #G2 #L2 #T1 #H
+  elim (teqx_fqu_trans … H … HU21) -H
+  /3 width=5 by fpb_fqu, ex3_2_intro/
+| #T1 #HUT1 #HnUT1
+  elim (teqx_cpx_trans … HU21 … HUT1) -HUT1
+  /6 width=5 by fpb_cpx, teqx_canc_sn, teqx_trans, ex3_2_intro/
+| /6 width=5 by fpb_lpx, rpx_teqx_div, teqx_reqx_conf, ex3_2_intro/
+]
+qed-.
+
+(* Basic_2A1: was just: lleq_fpb_trans *)
+lemma reqx_fpb_trans: ∀h,F,K1,K2,T. K1 ≛[T] K2 →
+                      ∀G,L2,U. ⦃F,K2,T⦄ ≻[h] ⦃G,L2,U⦄ →
+                      ∃∃L1,U0. ⦃F,K1,T⦄ ≻[h] ⦃G,L1,U0⦄ & U0 ≛ U & L1 ≛[U] L2.
+#h #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
+[ #G #L2 #U #H2 elim (reqx_fqu_trans … H2 … HT) -K2
+  /3 width=5 by fpb_fqu, ex3_2_intro/
+| #U #HTU #HnTU elim (reqx_cpx_trans … HT … HTU) -HTU
+  /5 width=11 by fpb_cpx, cpx_reqx_conf_sn, teqx_trans, teqx_reqx_conf, ex3_2_intro/ (**) (* time: 36s on dev *)
+| #L2 #HKL2 #HnKL2 elim (reqx_lpx_trans … HKL2 … HT) -HKL2
+  /6 width=5 by fpb_lpx, (* 2x *) reqx_canc_sn, ex3_2_intro/
+]
+qed-.