more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_jsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_jsx.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_computation/jsx.ma".
+
+(* COMPATIBILITY OF STRONG NORMALIZATION FOR UNBOUND RT-TRANSITION **********)
+
+(* Main properties **********************************************************)
+
+theorem jsx_fix (h) (G):
+        ∀f,L1,L. G ⊢ L1 ⊒[h,f] L → ∀L2. G ⊢ L ⊒[h,f] L2 → L = L2.
+#h #G #f #L1 #L #H elim H -f -L1 -L
+[ #f #L2 #H
+  >(jsx_inv_atom_sn … H) -L2 //
+| #f #I #K1 #K2 #_ #IH #L2 #H
+  elim (jsx_inv_push_sn … H) -H /3 width=1 by eq_f2/
+| #f #I #K1 #K2 #_ #IH #L2 #H
+  elim (jsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
+| #f #I #K1 #K2 #V #_ #_ #IH #L2 #H
+  elim (jsx_inv_unit_sn … H) -H /3 width=1 by eq_f2/
+]
+qed-.
+
+theorem jsx_trans (h) (G): ∀f. Transitive … (jsx h G f).
+#h #G #f #L1 #L #H1 #L2 #H2
+<(jsx_fix … H1 … H2) -L2 //
+qed-.