update in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_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/s_transition/fqu_teqg.ma".
+include "static_2/static/feqg.ma".
+include "basic_2/rt_transition/fpb_reqg.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with generic equivalence for closures *************************)
+
+(* Basic_2A1: uses: fleq_fpb_trans *)
+lemma feqg_fpb_trans (S):
+      reflexive … S → symmetric … S → Transitive … S →
+      ∀F1,F2,K1,K2,T1,T2. ❪F1,K1,T1❫ ≛[S] ❪F2,K2,T2❫ →
+      ∀G2,L2,U2. ❪F2,K2,T2❫ ≻ ❪G2,L2,U2❫ →
+      ∃∃G1,L1,U1. ❪F1,K1,T1❫ ≻ ❪G1,L1,U1❫ & ❪G1,L1,U1❫ ≛[S] ❪G2,L2,U2❫.
+#S #H1S #H2S #H3S #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
+#K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
+elim (teqg_fpb_trans … HT12 … H12) -T2 // #K0 #T0 #H #HT0 #HK0
+elim (reqg_fpb_trans … HK12 … H) -K2 // #L0 #U0 #H #HUT0 #HLK0
+@(ex2_3_intro … H) -H (**) (* full auto too slow *)
+/4 width=5 by feqg_intro_dx, reqg_trans, teqg_reqg_conf_sn, teqg_trans/
+qed-.
+
+(* Inversion lemmas with generic equivalence for closures *******************)
+
+(* Basic_2A1: uses: fpb_inv_fleq *)
+lemma fpb_inv_feqg (S):
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥.
+#S #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+[ #G2 #L2 #T2 #H12 #H elim (feqg_inv_gen_sn … H) -H
+  /3 width=11 by reqg_fwd_length, fqu_inv_teqg/
+| #T2 #_ #HnT #H elim (feqg_inv_gen_sn … H) -H /3 width=2 by teqg_teqx/
+| #L2 #_ #HnL #H elim (feqg_inv_gen_sn … H) -H /3 width=2 by reqg_reqx/
+]
+qed-.