# File TrivEx.ML

    (*  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";