## Mathematical English Usage - a Dictionary

## lemma

[*pl.* lemmas or lemmata]

We shall prove this theorem shortly, but first we need a key lemma.

The proof will be divided into a sequence of lemmas.

We now prove a lemma which is interesting in its own right.

The interest of the lemma is in the assertion that ......

We defer the proof of the “moreover” statement in Theorem 5 until after the proof of the lemma.

With Lemma 4 in $\langle$at$\rangle$ hand, we can finally define $E$ to be equal to $P(m)/H$.

......, from which it is an easy step, via Lemma 1, to the conclusion that ......

The following lemma is the key to extending Wagner's results.

The following lemma, crucial to Theorem 2, is also implicit in [4].

Note that this lemma does not give a simple criterion for deciding whether a given topology is indeed of the form $T_f$.

At first glance Lemma 2 seems to yield four possible outcomes.

The final lemma is due to F. Black and is included with his kind permission.

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