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The phrase "has shown to" is correct and usable in written English.
It is typically used when referring to the results of an experiment or observation, implying that something has been demonstrated or proved. Example: The study has shown to be effective in reducing stress levels among college students.
Exact(58)
And she has shown to have them all".
Biosilicate® has shown to be a very versatile, multipurpose biomaterial.
Test case prioritization (TCP) has shown to improve test effectiveness.
On the contrary, it has shown to improve it.
Bioluminescence imaging (BLI) has shown to be crucial for monitoring in vivo biological processes.
Nevertheless, reform is overdue and progress has shown to be a painstakingly slow process.
Such training has shown to reduce antibiotics prescribing rates by as much as 62%.
He gave some clear, very clear evidence yesterday which has shown to be wrong.
Then there is the willingness Trump has shown to put former vocal rivals in key slots.
In schools, more robust natural light has shown to improve test scores and reduce absenteeism.
Surface charge of NDs has shown to have a substantial affect on protein adsorption60.
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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