update in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma
new file mode 100644 (file)
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--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_feqg.ma
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.ma".
+include "basic_2/rt_transition/cpx_reqg.ma".
+include "basic_2/rt_transition/rpx_reqg.ma".
+
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS **************)
+
+(* Properties with generic equivalence for closures *************************)
+
+(**) (* to update *)
+lemma feqg_cpx_trans (S):
+      reflexive … S → symmetric … S →
+      ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T❫ →
+      ∀T2. ❪G2,L2❫ ⊢ T ⬈ T2 →
+      ∃∃T0. ❪G1,L1❫ ⊢ T1 ⬈ T0 & ❪G1,L1,T0❫ ≛[S] ❪G2,L2,T2❫.
+#S #H1S #H2S #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
+elim (feqg_inv_gen_dx … H) -H // #H #HL12 #HT1 destruct
+lapply (reqg_cpx_trans … HL12 … HT2) // #H
+lapply (cpx_reqg_conf_dx … HT2 … HL12) -HT2 -HL12 // #HL12
+lapply (teqg_cpx_trans … HT1 … H) -T // #HT12
+/4 width=4 by feqg_intro_sn, teqg_refl, ex2_intro/
+qed-.