update in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_feqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_feqg.ma
new file mode 100644 (file)
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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_computation/fsb.ma".
+
+(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
+
+(* Properties with generic equivalence for closures *************************)
+
+lemma fsb_feqg_trans (S):
+      reflexive … S → symmetric … S → Transitive … S →
+      ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+      ∀G2,L2,T2. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
+#S #H1S #H2S #H3S #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+#G1 #L1 #T1 #_ #IH #G2 #L2 #T2 #H12
+@fsb_intro #G #L #T #H2
+elim (feqg_fpb_trans … H12 … H2) -G2 -L2 -T2
+/2 width=5 by/
+qed-.