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The expression "and by inference" is correct and commonly used in written English.
It is typically used to introduce a statement that can be inferred or deduced from something previously mentioned. Example: "The suspect was seen near the crime scene and by inference, he is the primary suspect in the case." This sentence implies that because the suspect was seen near the crime scene, it can be inferred that he is the primary suspect. Another example: "The company's profits have been declining for the past three years and by inference, they will have to make significant changes in their business strategy." This sentence suggests that the declining profits will lead the company to make changes in their strategy.
Exact(58)
He, and by inference the government, are instinctively anti-bike.
He criticized himself -- and, by inference, other writers -- for an emotional detachment.
It was what Ridley and, by inference, even Margaret Thatcher thought best.
Pakistan's support for the Taliban, and by inference for Mr. bin Laden and the terrorist organization, only made things worse.
The fact of having capital is, in itself, considered a nearly Darwinian marker of success and, by inference, virility.
This means that the error in measuring its momentum (and, by inference, its velocity) would be enormous.
Rush did not hesitate to mock Obama as inauthentic — and, by inference, insufficiently black.
Mrs. Tomlin said a move to a wealthier and, by inference, white neighborhood would raise a number of uncomfortable questions: "Do you really want to break the barrier?
I merely had to receive orders and relay information for my Lord Vader and, by inference, for the teenagers gathered on the parlour carpet.
Similar(2)
We have measured the effects of regionally increased metabolic activity--and by inference electrical activity--on cortical growth in the developing rat brain.
Rather than soaring toward record levels, sunspots--and by inference their accompanying disruptive solar storms--will most likely increase to near-average peak levels by 2012.
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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