#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## key

[*see also*: basic, critical, crucial, essential, main

The key observation is that if......

The key part is to show that the submanifolds U_{k} fit together to form a complex submanifold.

A key step in obtaining (6) is Hölder's inequality.

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

It supplies the key to the proof of Theorem 2.

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

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