milestone update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / fpb / fpbc_reqg.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpbc_reqg.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpbc_reqg.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpbc_reqg.etc
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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/reqg_fqus.ma".
+include "basic_2/rt_transition/cpx_reqg.ma".
+include "basic_2/rt_transition/lpx_reqg.ma".
+include "basic_2/rt_transition/fpbc.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with generic equivalence for local environments ***************)
+
+(* Basic_2A1: was: teqg_fpb_trans *)
+lemma teqg_fpbc_trans (S):
+      reflexive … S → symmetric … S →
+      ∀U2,U1. U2 ≛[S] U1 →
+      ∀G1,G2,L1,L2,T1. ❪G1,L1,U1❫ ≻ ❪G2,L2,T1❫ →
+      ∃∃L,T2. ❪G1,L1,U2❫ ≻ ❪G2,L,T2❫ & T2 ≛[S] T1 & L ≛[S,T1] L2.
+#S #H1S #H2S #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 #H
+elim (fpbc_inv_gen S … H) -H #H12 #Hn12
+
+(* Basic_2A1: was just: lleq_fpb_trans *)
+lemma reqg_fpb_trans (S):
+      reflexive … S → symmetric … S →
+      ∀F,K1,K2,T. K1 ≛[S,T] K2 →
+      ∀G,L2,U. ❪F,K2,T❫ ≻ ❪G,L2,U❫ →
+      ∃∃L1,U0. ❪F,K1,T❫ ≻ ❪G,L1,U0❫ & U0 ≛[S] U & L1 ≛[S,U] L2.
+#S #H1S #H2S #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
+[ #G #L2 #U #H2 elim (reqg_fqu_trans … H2 … HT) -K2
+  /3 width=5 by fpb_fqu, ex3_2_intro/
+| #U #HTU #HnTU lapply (reqg_cpx_trans … HT … HTU) -HTU //
+  /4 width=8 by fpb_cpx, cpx_reqg_conf_sn, teqg_refl, ex3_2_intro/
+| #L2 #HKL2 #HnKL2 elim (reqg_lpx_trans … HKL2 … HT) -HKL2 //
+  /6 width=9 by fpb_lpx, reqg_reqx, reqg_repl, teqg_refl, ex3_2_intro/
+]
+qed-.