(* *)
(**************************************************************************)
-include "static_2/syntax/sh.ma".
+include "static_2/syntax/sh_nexts.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
+(**) (* use extensional equivalence *)
+ sh_nexts_inj: ∀s,n1,n2. ⇡*[h,n1]s = ⇡*[h,n2]s → n1 = n2
}.
(* decidability condition *)
record sh_decidable (h): Prop ≝
{
- nexts_dec: ∀s1,s2. Decidable (∃n. (next h)^n s1 = s2)
+ sh_nexts_dec: ∀s1,s2. Decidable (∃n. ⇡*[h,n]s1 = s2)
}.