(*  Title:      HOLCF/IOA/TrivEx.thy
    ID:         $Id: TrivEx.ML,v 1.5 2004/06/21 08:26:09 kleing Exp $
    Author:     Olaf Müller

Trivial Abstraction Example.
*)

Goalw [is_abstraction_def] 
"is_abstraction h_abs C_ioa A_ioa";
by (rtac conjI 1);
(* ------------- start states ------------ *)
by (simp_tac (simpset() addsimps 
    [h_abs_def,starts_of_def,C_ioa_def,A_ioa_def]) 1);
(* -------------- step case ---------------- *)
by (REPEAT (rtac allI 1));
by (rtac imp_conj_lemma 1);
by (simp_tac (simpset() addsimps [trans_of_def,
        C_ioa_def,A_ioa_def,C_trans_def,A_trans_def])1);
by (induct_tac "a" 1);
by (simp_tac (simpset() addsimps [h_abs_def]) 1);
qed"h_abs_is_abstraction";


Goal "validIOA C_ioa (<>[] <%(n,a,m). n~=0>)";
by (rtac AbsRuleT1 1);
by (rtac h_abs_is_abstraction 1);
by (rtac MC_result 1);
by (abstraction_tac 1);
by (asm_full_simp_tac (simpset() addsimps [h_abs_def]) 1);
qed"TrivEx_abstraction";


