(*  Title:      CCL/Fix.thy
    ID:         $Id: Fix.thy,v 1.4 2005/09/17 15:35:27 wenzelm Exp $
    Author:     Martin Coen
    Copyright   1993  University of Cambridge
*)

header {* Tentative attempt at including fixed point induction; justified by Smith *}

theory Fix
imports Type
begin

consts
  idgen      ::       "[i]=>i"
  INCL      :: "[i=>o]=>o"

axioms
  idgen_def:
  "idgen(f) == lam t. case(t,true,false,%x y.<f`x, f`y>,%u. lam x. f ` u(x))"

  INCL_def:   "INCL(%x. P(x)) == (ALL f.(ALL n:Nat. P(f^n`bot)) --> P(fix(f)))"
  po_INCL:    "INCL(%x. a(x) [= b(x))"
  INCL_subst: "INCL(P) ==> INCL(%x. P((g::i=>i)(x)))"

ML {* use_legacy_bindings (the_context ()) *}

end