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The phrase "assumption is that" is grammatically correct and can be used in written English.
It is typically used to introduce a statement that is based on a belief or assumption. Example: The assumption is that studying hard and getting good grades will lead to a successful career.
Exact(60)
"But my assumption is that will come," he said.
The assumption is that you have It.
The underlying assumption is that links convey recommendations.
"The assumption is that this is a pause," said Mudie.
My assumption is that it's people who will never farm".
The natural assumption is that Mr. Knight is wrong.
The assumption is that more money will buy the election.
The assumption is that the qualifiers will not.
The assumption is that pricing matters more as adoption increases.
"Our assumption is that he's benefiting from the drug trade".
The assumption is that equality is what we all want.
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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