cleanup for Fun.thy:
merged Update.{thy|ML} into Fun.{thy|ML}
moved o_def from HOL.thy to Fun.thy
added Id_def to Fun.thy
moved image_compose from Set.ML to Fun.ML
moved o_apply and o_assoc from simpdata.ML to Fun.ML
moved fun_upd_same and fun_upd_other (from Map.ML) to Fun.ML
added fun_upd_twist to Fun.ML
(* Title: HOL/Divides.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
The division operators div, mod and the divides relation "dvd"
*)
Divides = Arith +
consts
div, mod :: [nat, nat] => nat (infixl 70)
dvd :: [nat,nat]=>bool (infixl 70)
defs
mod_def "m mod n == wfrec (trancl pred_nat)
(%f j. if j<n then j else f (j-n)) m"
div_def "m div n == wfrec (trancl pred_nat)
(%f j. if j<n then 0 else Suc (f (j-n))) m"
dvd_def "m dvd n == EX k. n = m*k"
end