milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_feqg.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/feqg_fqup.ma".
+include "basic_2/rt_transition/fpb_feqg.ma".
+include "basic_2/rt_computation/fpbs_fqup.ma".
+
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
+
+(* Propreties with generic equivalence on referred closures *****************)
+
+(* Basic_2A1: uses: lleq_fpbs fleq_fpbs *)
+lemma feqg_fpbs (S) (G1) (G2) (L1) (L2) (T1) (T2):
+      reflexive … S → symmetric … S →
+      ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=5 by fpb_fpbs, feqg_fpb/ qed.
+
+(* Basic_2A1: uses: fpbs_lleq_trans *)
+lemma fpbs_feqg_trans (S) (G) (L) (T):
+      reflexive … S → symmetric … S →
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ ≛[S] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=9 by fpbs_strap1, feqg_fpb/ qed-.
+
+(* Basic_2A1: uses: lleq_fpbs_trans *)
+lemma feqg_fpbs_trans (S) (G) (L) (T):
+      reflexive … S → symmetric … S →
+      ∀G2,L2,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=5 by fpbs_strap2, feqg_fpb/ qed-.
+
+lemma teqg_fpbs_trans (S) (T):
+      reflexive … S → symmetric … S →
+      ∀T1. T1 ≛[S] T →
+      ∀G1,G2,L1,L2,T2. ❪G1,L1,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=8 by feqg_fpbs_trans, teqg_feqg/ qed-.
+
+lemma fpbs_teqg_trans (S) (T):
+      reflexive … S → symmetric … S →
+      ∀G1,G2,L1,L2,T1. ❪G1,L1,T1❫ ≥ ❪G2,L2,T❫ →
+      ∀T2. T ≛[S] T2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=8 by fpbs_feqg_trans, teqg_feqg/ qed-.