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"wrongly imply" is correct and can be used in written English.
It means to suggest or insinuate something incorrectly or falsely. Example: The newspaper article wrongly implies that the new mayor is corrupt without any evidence to support such a claim. In this sentence, "wrongly implies" is used to indicate that the implication made by the newspaper article is incorrect or inaccurate.
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Leo Winkley (@LeoWinkley) Headmaster, St Peter's school, York Tristram Hunt joins the list of those who wrongly imply that private education is a financial burden on the state and thus can be financially sanctioned in the cause of its social aspirations.
Prior cast it using this variant of RM: If ⊢ p → q then ⊢ IMq → IMp (the impermissibility of Smith being robbed then appears to wrongly imply the impermissibility of helping him who has been robbed).
The various forms of eliminativism wrongly imply that there are no statues; the doctrine of plenitude wrongly implies that there are incars; the doctrine of arbitrary undetached parts wrongly implies that there are leg-complements; and so forth.
(They wrongly imply that the stock market is in a bubble, by noting its record high. In fact, if the stock market had risen in step with the trend growth of the economy, it would still be 10-20 percent below its 2007 level).
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Nor is it, as Houston's title wrongly implies, a curiosity.
An earlier version wrongly implied that the main session was specifically about the selling of private health insurance.
The panel said the instructions wrongly implied that all jurors had to agree on mitigating circumstances to avoid issuing a death penalty.
Jefferies eventually received libel payouts from eight newspapers, including the Sun, because the titles had wrongly implied he could have been guilty.
I am pleased at the explicit acknowledgement that I neither sought, expected, nor received any financial gain that was being widely and wrongly implied.
More recently, the Canadian philosopher Charles Taylor maintained that the libertarian emphasis on the rights of the individual wrongly implies "the self-sufficiency of man alone".
But the dollar may not be weak enough for that even against the yen.Correction: We wrongly implied that foreign reserves are necessary to intervene to weaken a currency.
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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