Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
in HOL.
(* 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 *)
(* ------------------------------------------------------------------------ *)
val refl_less_fun = prove_goalw Fun1.thy [less_fun_def] "less_fun(f,f)"
(fn prems =>
[
(fast_tac (HOL_cs addSIs [refl_less]) 1)
]);
val antisym_less_fun = prove_goalw Fun1.thy [less_fun_def]
"[|less_fun(f1,f2); less_fun(f2,f1)|] ==> f1 = f2"
(fn prems =>
[
(cut_facts_tac prems 1),
(rtac (expand_fun_eq RS ssubst) 1),
(fast_tac (HOL_cs addSIs [antisym_less]) 1)
]);
val trans_less_fun = prove_goalw Fun1.thy [less_fun_def]
"[|less_fun(f1,f2); less_fun(f2,f3)|] ==> less_fun(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))
]);
(*
--------------------------------------------------------------------------
Since less_fun :: "['a::term=>'b::po,'a::term=>'b::po] => bool" the
lemmas refl_less_fun, antisym_less_fun, trans_less_fun justify
the class arity fun::(term,po)po !!
--------------------------------------------------------------------------
*)