#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## proceed

[*see also*: act, operate, continue, pursue, move, turn

The proof proceeds along the same lines as the proof of Theorem 4.

The standard proofs proceed via the Cauchy formula.

We now proceed to matrix rings.

In Section 3 we proceed with the study of...... [= start or continue the
study]

We shall proceed without making explicit distinctions between the two types of
convergence.

Proceeding further in this direction, we obtain the following corollary.

Proceeding as in the proof of......, let......

Before proceeding we record an inequality for the size of an admissible X.

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