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I added a link to EoM at Lie’s three theorems, where there is a statement of the first theorem - we just had the slightly disparaging sentence
…is today regarded as lacking a good notion of differentiable manifold.
There is (or was) still some awkwardness in the article, some of it attributable (as far as I can tell) to the fact that all three of the original Lie theorems were local in nature, and the reformulations in terms of global Lie groups only came later, at least for Lie II and Lie III. It would help to clarify this point at the outset.
I have tried to rewrite the article to smooth some of this out, and fix some minor errors. But some residual awkwardness may still remain; those with greater expertise should look.
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