src/CCL/fix.thy

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(*  Title: 	CCL/Lazy/fix.thy
    ID:         $Id$
    Author: 	Martin Coen
    Copyright   1993  University of Cambridge

Tentative attempt at including fixed point induction.
Justified by Smith.
*)

Fix = Type + 

consts

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

rules

  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)))"

end