equal
deleted
inserted
replaced
4 Copyright 1994 TU Muenchen |
4 Copyright 1994 TU Muenchen |
5 |
5 |
6 Some general lemmas |
6 Some general lemmas |
7 *) |
7 *) |
8 |
8 |
9 goal Sorting.thy "!x. mset (xs@ys) x = mset xs x + mset ys x"; |
9 Goal "!x. mset (xs@ys) x = mset xs x + mset ys x"; |
10 by (list.induct_tac "xs" 1); |
10 by (list.induct_tac "xs" 1); |
11 by (ALLGOALS Asm_simp_tac); |
11 by (ALLGOALS Asm_simp_tac); |
12 qed "mset_append"; |
12 qed "mset_append"; |
13 |
13 |
14 goal Sorting.thy "!x. mset [x:xs. ~p(x)] x + mset [x:xs. p(x)] x = \ |
14 Goal "!x. mset [x:xs. ~p(x)] x + mset [x:xs. p(x)] x = \ |
15 \ mset xs x"; |
15 \ mset xs x"; |
16 by (list.induct_tac "xs" 1); |
16 by (list.induct_tac "xs" 1); |
17 by (ALLGOALS Asm_simp_tac); |
17 by (ALLGOALS Asm_simp_tac); |
18 qed "mset_compl_add"; |
18 qed "mset_compl_add"; |
19 |
19 |
20 Addsimps [mset_append, mset_compl_add]; |
20 Addsimps [mset_append, mset_compl_add]; |
21 |
21 |
22 goal Sorting.thy "set xs = {x. mset xs x ~= 0}"; |
22 Goal "set xs = {x. mset xs x ~= 0}"; |
23 by (list.induct_tac "xs" 1); |
23 by (list.induct_tac "xs" 1); |
24 by (ALLGOALS Asm_simp_tac); |
24 by (ALLGOALS Asm_simp_tac); |
25 by (Fast_tac 1); |
25 by (Fast_tac 1); |
26 qed "set_via_mset"; |
26 qed "set_via_mset"; |
27 |
27 |