equal
deleted
inserted
replaced
43 |
43 |
44 Goal "lfp(univ(0), %x. Con2(x,x)) : counit2"; |
44 Goal "lfp(univ(0), %x. Con2(x,x)) : counit2"; |
45 by (rtac (singletonI RS counit2.coinduct) 1); |
45 by (rtac (singletonI RS counit2.coinduct) 1); |
46 by (rtac (qunivI RS singleton_subsetI) 1); |
46 by (rtac (qunivI RS singleton_subsetI) 1); |
47 by (rtac ([lfp_subset, empty_subsetI RS univ_mono] MRS subset_trans) 1); |
47 by (rtac ([lfp_subset, empty_subsetI RS univ_mono] MRS subset_trans) 1); |
48 by (fast_tac (claset() addSIs [Con2_bnd_mono RS lfp_Tarski]) 1); |
48 by (fast_tac (claset() addSIs [Con2_bnd_mono RS lfp_unfold]) 1); |
49 qed "lfp_Con2_in_counit2"; |
49 qed "lfp_Con2_in_counit2"; |
50 |
50 |
51 (*Lemma for proving finality. Borrowed from ex/llist_eq.ML!*) |
51 (*Lemma for proving finality. Borrowed from ex/llist_eq.ML!*) |
52 Goal "Ord(i) ==> ALL x y. x: counit2 & y: counit2 --> x Int Vset(i) <= y"; |
52 Goal "Ord(i) ==> ALL x y. x: counit2 & y: counit2 --> x Int Vset(i) <= y"; |
53 by (etac trans_induct 1); |
53 by (etac trans_induct 1); |