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I have a theorem of the following form

Definition. An object $y$ has property $X$ if... [2 lines...]

Lemma. If $y$ has property $X$, then ...

I could also simply write

Lemma. If $y$ has the property that [insert definition of $X$], then

But the definition of $X$ is long enough that writing it this way would be clumsy.

On the other hand, the definition of $X$ is only used in this lemma, so it should not draw too much attention, so what would be a good-writing-style of making the definition of $X$ take less attention while still using it to keep the lemma short? ($X$ has an intuitive english-language term).

I though of putting the definition in the proof of the Lemma but this comes accross as non-rigorous.

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user56834
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    I would definitely just write it under the assumptions of the lemma, not as a separate definition, if it's never used outside of the lemma, and if it's not a standard definition. – MSDG Aug 31 '18 at 17:54
  • Maybe your definition will be important for someone else who will read your paper. – paf Aug 31 '18 at 17:56
  • @Sobi, how would you do it so that it's still possible to state the lemma in an intuitive natural language and succinct way? Note that my definition $X$ has an intuitive english-language meaning. – user56834 Aug 31 '18 at 19:15
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    @Programmer2134 How about writing one possibly less formal sentence before the lemma (or between the lemma and the proof)? When I write, I try to keep my theorems and proofs quite dry and rigorous (i.e. no intuitive explanations), and I try to give some intuition before stating them. – MSDG Aug 31 '18 at 19:19

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