milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbc_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbc_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 "basic_2/rt_transition/fpb_feqg.ma".
+include "basic_2/rt_transition/fpbc.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with generic equivalence for closures *************************)
+
+(* Basic_2A1: uses: teqg_fpb_trans lleq_fpb_trans fleq_fpb_trans *)
+lemma feqg_fpbc_trans (S) (G) (L) (T):
+      reflexive … S → symmetric … S → Transitive … S →
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ ≻ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
+#S #G #L #T #H1S #H2S #H3S #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
+elim (fpbc_inv_gen sfull … H2) -H2 #H2 #Hn2
+/6 width=9 by fpbc_intro, feqg_fpb_trans, feqg_canc_sn, feqg_feqx/
+qed-.
+
+(* Inversion lemmas with generic equivalence for closures *******************)
+
+(* Basic_2A1: uses: fpb_inv_fleq *)
+lemma fpbc_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 #H #H12
+elim (fpbc_inv_gen S … H) -H #_ #Hn2
+/2 width=1 by/
+qed-.