src/HOLCF/fun1.ML

{HOL,ZF}/indrule/quant_induct: replaced ssubst in eresolve_tac by
separate call to hyp_subst_tac. This avoids substituting in x=f(x)

{HOL,ZF}/indrule/ind_tac: now tries resolve_tac [refl]. This handles
trivial equalities such as x=a.

{HOL,ZF}/intr_elim/intro_tacsf_tac: now calls assume_tac last, to try refl
before any equality assumptions

(*  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 !!
 -------------------------------------------------------------------------- 
*)