Text Formatting ⇒ lemma numbering across sections

[nullgraph]

Hi, I'm using package amsthm. My theorem is in section 1. I want to number my theorem such that it has the section number, so I used:

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 \newtheorem{theorem}{Theorem}[section]

So my theorem is called Theorem 1.1
Now in section 2, I have my lemma, but I also want my lemma to use the theorem counter (i.e. it should be called Lemma 1.2), so I did:

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\newtheorem{lemma}[theorem]{Lemma}

But instead of following the theorem counter, it seems that the section counter inherited from theorem took over, so my lemma is numbered as Lemma 2.1. Is there any way to number my lemma after my theorem consistently across different sections? I'm thinking of maybe setting the lemma counter manually, but then it wouldn't reference the theorem counter. Another fix that would work for me is Theorem 1.1 and then Lemma 1.1.1 (still in a different section), but I don't know how to do that.

Any help greatly appreciated!

[youngprof]

The optional argument in brackets for you [section] sets the counter to reset itself when you switch sections. If you are fine with theorems,lemmas, etc numbered continuously throughout the document just leave the brackets empty; similarly, to get the 1.1.1 sort of numbering use the optional argument [subsection]. If you want just a single theorem to be not reset across the section break but everything else to change numbers I think you'll have to do it manually.