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LyX has built-in all kinds of inserts for Math. Does LyX have some ready commands or GUI buttons to get environments for things such as proofs, lemmas and theorems? What is procedure to create for example a lemma in Lyx: do you create a paragraph or do you select some settings under Insert > Math or elsewhere?

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where I have loaded the Theorems (AMS) module as instructed here for independent numbering for proofs, lemmas and others.

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Having added a module, you'll find all the different environments in the style drop down menu in the top left, where you also find e.g. sections and such.

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