#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## upon

The second inequality follows upon considering R_{i} for i>0.

We may assume, upon replacing F by F_{1}, that......

Upon combining the estimate for B with (5), we have now established
the first conclusion of Theorem 8.

Adding E to both sides of (1), we can call upon (2) to obtain (3).

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