src/HOL/Nat.thy
author berghofe
Tue, 30 May 2000 18:02:49 +0200
changeset 9001 93af64f54bf2
parent 7702 35c7e0df749f
child 9436 62bb04ab4b01
permissions -rw-r--r--
the is now defined using primrec, avoiding explicit use of arbitrary.

(*  Title:      HOL/Nat.thy
    ID:         $Id$
    Author:     Tobias Nipkow
    Copyright   1997 TU Muenchen

Type "nat" is a linear order, and a datatype
*)

Nat = NatDef + Inductive +

rep_datatype nat
  distinct Suc_not_Zero, Zero_not_Suc
  inject   Suc_Suc_eq
  induct   nat_induct

instance nat :: order (le_refl,le_trans,le_anti_sym,nat_less_le)
instance nat :: linorder (nat_le_linear)

consts
  "^"           :: ['a::power,nat] => 'a            (infixr 80)

end