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The phrase 'with this assumption' is grammatically correct and can be used in written English.
You can use it when you need to introduce the idea that something is being accepted as true for the purpose of argument or analysis. For example: "With this assumption, we can analyze the current economic trends."
Exact(60)
With this assumption, all directions grow at the same pace to maintain the spherical symmetry.
But there's a problem with this assumption.
Do you agree or disagree with this assumption?
There are a few problems with this assumption, though.
"But we have to be careful with this assumption about games and attention span," she says.
And the problem with this assumption is that turns scientists into the very thing they were supposed to be replacing.
Animal studies are consistent with this assumption.
The creatability requirement must be compatible with this assumption.
Accordingly, no atomless mereology is compatible with this assumption.
With this assumption, many results can be obtained analytically.
Several rate constants were estimated with this assumption.
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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