src/ZF/ex/Acc.ML
changeset 2469 b50b8c0eec01
parent 1461 6bcb44e4d6e5
child 4091 771b1f6422a8
equal deleted inserted replaced
2468:428efffe8599 2469:b50b8c0eec01
    15   Otherwise acc(r) would be a proper class!    *)
    15   Otherwise acc(r) would be a proper class!    *)
    16 
    16 
    17 (*The intended introduction rule*)
    17 (*The intended introduction rule*)
    18 val prems = goal Acc.thy
    18 val prems = goal Acc.thy
    19     "[| !!b. <b,a>:r ==> b: acc(r);  a: field(r) |] ==> a: acc(r)";
    19     "[| !!b. <b,a>:r ==> b: acc(r);  a: field(r) |] ==> a: acc(r)";
    20 by (fast_tac (ZF_cs addIs (prems@acc.intrs)) 1);
    20 by (fast_tac (!claset addIs (prems@acc.intrs)) 1);
    21 qed "accI";
    21 qed "accI";
    22 
    22 
    23 goal Acc.thy "!!a b r. [| b: acc(r);  <a,b>: r |] ==> a: acc(r)";
    23 goal Acc.thy "!!a b r. [| b: acc(r);  <a,b>: r |] ==> a: acc(r)";
    24 by (etac acc.elim 1);
    24 by (etac acc.elim 1);
    25 by (fast_tac ZF_cs 1);
    25 by (Fast_tac 1);
    26 qed "acc_downward";
    26 qed "acc_downward";
    27 
    27 
    28 val [major,indhyp] = goal Acc.thy
    28 val [major,indhyp] = goal Acc.thy
    29     "[| a : acc(r);                                             \
    29     "[| a : acc(r);                                             \
    30 \       !!x. [| x: acc(r);  ALL y. <y,x>:r --> P(y) |] ==> P(x) \
    30 \       !!x. [| x: acc(r);  ALL y. <y,x>:r --> P(y) |] ==> P(x) \
    31 \    |] ==> P(a)";
    31 \    |] ==> P(a)";
    32 by (rtac (major RS acc.induct) 1);
    32 by (rtac (major RS acc.induct) 1);
    33 by (rtac indhyp 1);
    33 by (rtac indhyp 1);
    34 by (fast_tac ZF_cs 2);
    34 by (Fast_tac 2);
    35 by (resolve_tac acc.intrs 1);
    35 by (resolve_tac acc.intrs 1);
    36 by (assume_tac 2);
    36 by (assume_tac 2);
    37 by (etac (Collect_subset RS Pow_mono RS subsetD) 1);
    37 by (etac (Collect_subset RS Pow_mono RS subsetD) 1);
    38 qed "acc_induct";
    38 qed "acc_induct";
    39 
    39 
    40 goal Acc.thy "wf[acc(r)](r)";
    40 goal Acc.thy "wf[acc(r)](r)";
    41 by (rtac wf_onI2 1);
    41 by (rtac wf_onI2 1);
    42 by (etac acc_induct 1);
    42 by (etac acc_induct 1);
    43 by (fast_tac ZF_cs 1);
    43 by (Fast_tac 1);
    44 qed "wf_on_acc";
    44 qed "wf_on_acc";
    45 
    45 
    46 (* field(r) <= acc(r) ==> wf(r) *)
    46 (* field(r) <= acc(r) ==> wf(r) *)
    47 val acc_wfI = wf_on_acc RS wf_on_subset_A RS wf_on_field_imp_wf;
    47 val acc_wfI = wf_on_acc RS wf_on_subset_A RS wf_on_field_imp_wf;
    48 
    48 
    50 by (rtac subsetI 1);
    50 by (rtac subsetI 1);
    51 by (etac (major RS wf_induct2) 1);
    51 by (etac (major RS wf_induct2) 1);
    52 by (rtac subset_refl 1);
    52 by (rtac subset_refl 1);
    53 by (rtac accI 1);
    53 by (rtac accI 1);
    54 by (assume_tac 2);
    54 by (assume_tac 2);
    55 by (fast_tac ZF_cs 1);
    55 by (Fast_tac 1);
    56 qed "acc_wfD";
    56 qed "acc_wfD";
    57 
    57 
    58 goal Acc.thy "wf(r) <-> field(r) <= acc(r)";
    58 goal Acc.thy "wf(r) <-> field(r) <= acc(r)";
    59 by (EVERY1 [rtac iffI, etac acc_wfD, etac acc_wfI]);
    59 by (EVERY1 [rtac iffI, etac acc_wfD, etac acc_wfI]);
    60 qed "wf_acc_iff";
    60 qed "wf_acc_iff";