Sentence examples for we replace with from inspiring English sources

For one thing, not every case of replacement counts as substitution: the expression we replace with its synonym within a larger expression must be a constituent of the larger expression.

If, we replace with.

First, we replace with the equivalent decision statistic.

for all and We replace with in (2.20) to obtain (2.21).

that is, we obtain the same expression in (2.4) if we replace with.

In the above proof, if we replace with, then the following result can be obtained.

It even had a hole in the wall for a coffee machine, which we replaced with our designed-to-fit pill dispenser.

With theorem 1.2, which we will present just below, we can replace with and with.

Since the imaging sampling interval is always a known constant, we can replace with in.

If we dispense with measurement-based management, what can we replace it with?

But what can we replace it with?