--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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.ma".
+
+(* SORT HIERARCHY ***********************************************************)
+
+(* acyclicity condition *)
+record sh_acyclic (h): Prop ≝
+{
+ nexts_inj: ∀s,n1,n2. (next h)^n1 s = (next h)^n2 s → n1 = n2
+}.
+
+(* decidability condition *)
+record sh_decidable (h): Prop ≝
+{
+ nexts_dec: ∀s1,s2. Decidable (∃n. (next h)^n s1 = s2)
+}.