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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.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/syntax/sh_props.ma".
+
+(* SORT HIERARCHY ***********************************************************)
+
+(* strict monotonicity condition *)
+record sh_lt (h): Prop ≝
+{
+  next_lt: ∀s. s < ⫯[h]s
+}.
+
+(* Basic properties *********************************************************)
+
+lemma nexts_le (h): sh_lt h → ∀s,n. s ≤ (next h)^n s.
+#h #Hh #s #n elim n -n [ // ] normalize #n #IH
+lapply (next_lt … Hh ((next h)^n s)) #H
+lapply (le_to_lt_to_lt … IH H) -IH -H /2 width=2 by lt_to_le/
+qed.
+
+lemma nexts_lt (h): sh_lt h → ∀s,n. s < (next h)^(↑n) s.
+#h #Hh #s #n normalize
+lapply (nexts_le … Hh s n) #H
+@(le_to_lt_to_lt … H) /2 width=1 by next_lt/
+qed.
+
+axiom sh_lt_dec (h): sh_lt h → sh_decidable h.
+
+axiom sh_lt_acyclic (h): sh_lt h → sh_acyclic h.