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I am using the Koma-script book class in Lyx. By default, theorems, definitions, lemmas, and so on, follow the same numbering. So after "Theorem 1" comes "Definition 2", then "Lemma 3", and so on, even though "Definition 2" is actually the first definition in the document.

I would like theorems and definitions to be numbered independently. How do I accomplish this (in Lyx)?

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Go to Document > Settings > Modules

Click on "Theorems (AMS, Numbered by Type)"

The description is as follows:

Defines theorem environments and the proof environment using
the extended AMS machinery. Both numbered and unnumbered
types are provided. Contrary to the plain AMS Theorem
module, the different theorem types provided here each have
a separate counter (e.g., theorem 1, theorem 2, lemma 1,
proposition 1, theorem 3, lemma 2, ..., as opposed to
theorem 1, theorem 2, lemma 3, proposition 4, ...). The
numbering's scope is the whole document. For chapter- and
section-wide numbering, use one of the 'within
Sections'/'within Chapters' modules, respectively.

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