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The phrase "any presumption that" is correct and can be used in written English.
It is often used in formal or academic writing to introduce a belief or assumption that may not be true or proven. Here is an example: Any presumption that all teenagers are lazy and irresponsible is unfair and disregards the hard work and success of many young people.
Exact(15)
No presumption that it is true, nor any presumption that it is not true.
And it erases any presumption that the anti-Government movement is limited to politically radical campuses in the hinterlands.
When there are "negative externalities" — costs that economic actors impose on others without paying a price for their actions — any presumption that the market economy, left to its own devices, will do the right thing goes out the window.
The Supreme Court has expressly rejected any presumption that a commercial use is unfair, and has held that a use which does not substitute for the original does not allow the inference of market harm as to the fourth factor.
Federalism, comity, and the constitutional obligation of state and federal courts all counsel against any presumption that a decision of this Court will "deter" lower federal or state courts from fully performing their sworn duty.
But she sets up straw men as examples: there is no proposal to punish people just for travelling to Syria or Iraq, nor any presumption that those who do are jihadis.
Similar(45)
There has been a presumption that XP users would make the switch.
However, this is only a presumption that cannot be proven by this retrospective analysis.
They created a presumption that any derogatory remark made about a gentleman must be false.
Is this based on a presumption that any association with culture will be electorally unhelpful with the tabloids ?
The current proposal, in carrying out the Dodd-Frank law, is based on a presumption that any possible risk-taking activity conducted by a financial institution in service to clients is prohibited proprietary trading until the institution can prove otherwise.
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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