Is there a standard way to manage sentences within a sentence? For example:

Using the following definition

Definition 1: A graph G is isomorphic to another graph H if there is an isomorphism f from the vertices of G to the vertices of H. Further, f(v)f(u) is an edge of H if and only if vu is an edge of G.

in the following lemma,

Lemma 2: Let H and G be isomorphic graphs. If there is a set of t vertices that disconnect H then there is a set of t vertices that disconnect G.

we obtain the following theorem

Theorem 3: Suppose H is isomorphic to G.  Then the connectivity of H is equal to the connectivity of G.

Is this grammatically correct, or should it be presented in a different way?

  • Although your question is clear and interesting, it may not be a good fit at this site because many participants here think that questions about formatting, punctuation, or spelling aren't really questions about English language and usage. (The implicit premise of this view is that formatting, punctuation, and spelling are features of written language, whereas grammar is a feature of spoken language.) From their perspective, you've asked a question that you say is about grammaticality—but they don't see any grammatical issue to answer. Hence the "needs details or clarity" criticism. ... – Sven Yargs Sep 2 '20 at 5:48
  • ... I can't offer a formal answer to your question because it has been closed, but in my view, you have already handled the sentences-within-a-sentence difficulty quite well. My only additional advice would be to indent the text blocks for Definition 1, Lemma 2, and Theorem 3 as display text blocks while leaving the linking segments of the sentence ("Using the following definition" and "in the following lemma," and "we obtain the following theorem") on separate lines that start flush left (not indented). You could add a colon after "theorem"—but otherwise I think the punctuation is fine as is. – Sven Yargs Sep 2 '20 at 5:49
  • I just voted to leave the question closed, because I believe that the stated close reason applies and has not been addressed  — I don’t understand what the question is.  What sentence(s) are within other sentence(s)?  What do you mean by “manage”?  Are you asking about grammaticality, sentence meaning, or what? – Scott Sep 2 '20 at 6:02
  • @SvenYargs: Why do you believe that the question is about formatting, punctuation or spelling?  The OP’s words are “How should I manage sentences within a sentence?” and “Is this grammatically correct …?”  The OP selected the tags “grammaticality” and “sentence-meaning”.  I don’t see anything about formatting, except for your contributions. – Scott Sep 2 '20 at 6:02
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    @SvenYargs Yes that's what I'm asking, basically if the definitions lemmas... are short e.g. Using the definition a=b and the lemma b<c, we get the theorem a<c. This seems fine. But what if the definition lemma and theorem themselves are several sentences long? is "Using the following definition [Definition 1 text block] in the following lemma [Lemma 2 text block] we obtain the following theorem [Theorem 3 text block]." a good idea or not? Or should I just state and label the theorems and refer to them by number in the sentence? – Hao S Sep 2 '20 at 7:25