(* Title: HOL/Update.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
Function updates: like theory Map, but for ordinary functions
*)
open Update;
goalw thy [update_def] "(f[x:=y] = f) = (f x = y)";
by Safe_tac;
by (etac subst 1);
by (rtac ext 2);
by Auto_tac;
qed "update_idem_iff";
(* f x = y ==> f[x:=y] = f *)
bind_thm("update_idem", update_idem_iff RS iffD2);
AddIffs [refl RS update_idem];
goal thy "(f[x:=y])z = (if x=z then y else f z)";
by (simp_tac (simpset() addsimps [update_def]) 1);
qed "update_apply";
Addsimps [update_apply];