How can I find the maximum element in a set of numbers (nat) in Isabelle. The max function doesn't work, as it is only defined to take the maximum of two elements. I have an idea of how I could implement it using a reduce like function, but I don't know how to pick one random element from a set.
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1Using sets if you really want to take about lists is pretty cumbersome and often makes the proofs longer. – Lars Noschinski Feb 13 '13 at 07:07
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The function you are looking for is called Max. If you are looking for basic constants the guide What's in Main from the official Isabelle documentation is often useful. There is also the find_consts command which can be used to search for functions by type.
Lars Noschinski
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Just to add to this: search for constants is also available from Isabelle/jEdit's query panel (see [3.4.2, p.30](https://isabelle.in.tum.de/dist/doc/jedit.pdf) in the Isabelle/jEdit manual). If you have an idea what your function's name—or a part of it—could be called you can write `name:
` to search for matching constants. Small caveat: the search is limited to the imported theories. In this case you would have to have theory `Lattices_Big` imported (which seems to be included transitively in `Main`). – FK82 Jun 28 '20 at 07:35
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If you follow the definition of Max to theory Big_Operators in the main HOL library, you will see that it is defined like this:
Max = fold1 max
The combinator fold1 is your "reduce like function" that works on finite sets.
See also theory Finite_Set and its locale folding for the mathematical background that is required here to fold over arbitrary sets, instead of concrete lists.
Makarius
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