(* Title: HOLCF/Fun1.ML
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
Lemmas for fun1.thy
*)
open Fun1;
(* ------------------------------------------------------------------------ *)
(* less_fun is a partial order on 'a => 'b *)
(* ------------------------------------------------------------------------ *)
qed_goalw "refl_less_fun" thy [less_fun_def] "(f::'a::term =>'b::po) << f"
(fn prems =>
[
(fast_tac (HOL_cs addSIs [refl_less]) 1)
]);
qed_goalw "antisym_less_fun" Fun1.thy [less_fun_def]
"[|(f1::'a::term =>'b::po) << f2; f2 << f1|] ==> f1 = f2"
(fn prems =>
[
(cut_facts_tac prems 1),
(stac expand_fun_eq 1),
(fast_tac (HOL_cs addSIs [antisym_less]) 1)
]);
qed_goalw "trans_less_fun" Fun1.thy [less_fun_def]
"[|(f1::'a::term =>'b::po) << f2; f2 << f3 |] ==> f1 << f3"
(fn prems =>
[
(cut_facts_tac prems 1),
(strip_tac 1),
(rtac trans_less 1),
(etac allE 1),
(atac 1),
((etac allE 1) THEN (atac 1))
]);