1 (* Title: HOLCF/IOA/TrivEx.thy
4 Copyright 1995 TU Muenchen
6 Trivial Abstraction Example
9 val prems = goal HOL.thy "(P ==> Q-->R) ==> P&Q --> R";
10 by (fast_tac (claset() addDs prems) 1);
14 Goalw [is_abstraction_def]
15 "is_abstraction h_abs C_ioa A_ioa";
17 (* ------------- start states ------------ *)
18 by (simp_tac (simpset() addsimps
19 [h_abs_def,starts_of_def,C_ioa_def,A_ioa_def]) 1);
20 (* -------------- step case ---------------- *)
21 by (REPEAT (rtac allI 1));
22 by (rtac imp_conj_lemma 1);
23 by (simp_tac (simpset() addsimps [trans_of_def,
24 C_ioa_def,A_ioa_def,C_trans_def,A_trans_def])1);
25 by (induct_tac "a" 1);
26 by (simp_tac (simpset() addsimps [h_abs_def]) 1);
27 qed"h_abs_is_abstraction";
30 Goal "validIOA C_ioa (<>[] <%(n,a,m). n~=0>)";
31 by (rtac AbsRuleT1 1);
32 by (rtac h_abs_is_abstraction 1);
33 by (rtac MC_result 1);
34 by (abstraction_tac 1);
35 by (asm_full_simp_tac (simpset() addsimps [h_abs_def]) 1);
36 qed"TrivEx_abstraction";