A lemma is a theorem used to simplify the proof of some other theorem. One might draw an analogy to the use of components in the construction of an electronic device -- no electronic device really "needs" separate components, but modular design greatly simplifies and stabilises.

When giving a lemma a name, one might say that the lemma is "towards" a given theorem. Then, when proving the main theorem, one might say "by the lemma" to draw on the result of the latter.

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