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The phrase "a second example shows that the" is correct and usable in written English.
It can be used when introducing another example that supports or illustrates a point being made in a discussion or argument.
Example: "In the previous section, we discussed the impact of climate change on agriculture. A second example shows that the rising temperatures are also affecting water supply in many regions."
Alternatives: "another example indicates that the" or "a further example demonstrates that the".
Exact(1)
A second example shows that the Finite Cell Method correctly captures the thermoelastic state of a complex problem from engineering practice.
Similar(59)
Our second example shows that the problem is not limited to inferences about the past.
The first example shows that the above mentioned condition is not necessary, while the second example provides a case for which it is a necessary condition.
The third example shows that the question has been responded to, that is, "draw the whole ribbon".
The first example shows that condition ' ϕ ( t ) < t for all t > 0 ' in Theorem 2 cannot be omitted.
The second line in the example shows that the address binding is an IP version 4 address.
An example shows that the first inequality in (9), to singular values, does not hold [6].
This example shows that the compactness theorem does not hold for second-order logic.
This example shows that the Löwenheim Skolem theorem does not hold for second-order logic.
The second example shows a region that includes a single CGI [ 57] encompassing TSSs of various POLR1B transcripts.
The first example shows a siRNA that promoted the downregulation of genes containing intragenic L1s, whereas the second shows a siRNA that promoted the upregulation of these genes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com