src/HOLCF/void.ML

isatool expandshort;

(*  Title: 	HOLCF/void.ML
    ID:         $Id$
    Author: 	Franz Regensburger
    Copyright   1993  Technische Universitaet Muenchen

Lemmas for void.thy.

These lemmas are prototype lemmas for class porder 
see class theory porder.thy
*)

open Void;

(* ------------------------------------------------------------------------ *)
(* A non-emptyness result for Void                                          *)
(* ------------------------------------------------------------------------ *)

val VoidI = prove_goalw Void.thy [UU_void_Rep_def,Void_def] 
 " UU_void_Rep : Void"
(fn prems =>
	[
	(rtac (mem_Collect_eq RS ssubst) 1),
	(rtac refl 1)
	]);

(* ------------------------------------------------------------------------ *)
(* less_void is a partial ordering on void                                  *)
(* ------------------------------------------------------------------------ *)

val refl_less_void = prove_goalw Void.thy [ less_void_def ] "less_void(x,x)"
(fn prems =>
	[
	(fast_tac HOL_cs 1)
	]);

val antisym_less_void = prove_goalw Void.thy [ less_void_def ] 
	"[|less_void(x,y); less_void(y,x)|] ==> x = y"
(fn prems =>
	[
	(cut_facts_tac prems 1),
	(rtac (Rep_Void_inverse RS subst) 1),
	(etac subst 1),
	(rtac (Rep_Void_inverse RS sym) 1)
	]);

val trans_less_void = prove_goalw Void.thy [ less_void_def ] 
	"[|less_void(x,y); less_void(y,z)|] ==> less_void(x,z)"
(fn prems =>
	[
	(cut_facts_tac prems 1),
	(fast_tac HOL_cs 1)
	]);

(* ------------------------------------------------------------------------ *)
(* a technical lemma about void:                                            *)
(* every element in void is represented by UU_void_Rep                      *)
(* ------------------------------------------------------------------------ *)

val unique_void = prove_goal Void.thy "Rep_Void(x) = UU_void_Rep"
(fn prems =>
	[
	(rtac (mem_Collect_eq RS subst) 1), 
	(fold_goals_tac [Void_def]),
	(rtac Rep_Void 1)
	]);