src/HOL/Isar_examples/KnasterTarski.thy
changeset 6893 6e56603fb339
parent 6884 a05159fbead0
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     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