9 theory KnasterTarski = Main:; |
9 theory KnasterTarski = Main:; |
10 |
10 |
11 |
11 |
12 theorems [dest] = monoD; (* FIXME [dest!!] *) |
12 theorems [dest] = monoD; (* FIXME [dest!!] *) |
13 |
13 |
14 (* |
14 text {* |
15 The proof of Knaster-Tarski below closely follows the presentation in |
15 The proof of Knaster-Tarski below closely follows the presentation in |
16 'Introduction to Lattices' and Order by Davey/Priestley, pages |
16 'Introduction to Lattices' and Order by Davey/Priestley, pages |
17 93--94. All of their narration has been rephrased in terms of formal |
17 93--94. All of their narration has been rephrased in terms of formal |
18 Isar language elements, except one stament only that has been left as |
18 Isar language elements, except one stament only that has been left as |
19 a comment. Also note that Davey/Priestley do not point out |
19 a comment. Also note that Davey/Priestley do not point out |
20 non-emptyness of the set @term{??H}, (which is obvious, but not |
20 non-emptyness of the set @term{??H}, (which is obvious, but not |
21 vacous). |
21 vacous). |
22 |
22 |
23 Just as many textbook-style proofs, there is a strong bias towards |
23 Just as many textbook-style proofs, there is a strong bias towards |
24 forward reasoning, with little hierarchical structure. |
24 forward reasoning, with little hierarchical structure. |
25 *) |
25 *}; |
26 |
26 |
27 theorem KnasterTarski: "mono f ==> EX a::'a set. f a = a"; |
27 theorem KnasterTarski: "mono f ==> EX a::'a set. f a = a"; |
28 proof; |
28 proof; |
29 assume mono: "mono f"; |
29 assume mono: "mono f"; |
30 |
30 |