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The phrase "definitively demonstrated" is correct and can be used in written English.
You can use it when you want to emphasize that something has been clearly and decisively proven. For example: "The effectiveness of the medication was definitively demonstrated in the clinical trials."
Exact(60)
It is probably lethal, although this has not been definitively demonstrated.
But until now the ocean's heat absorption had not been definitively demonstrated, and its magnitude had not been determined.
And Jerry Lewis and Jacques Tati — and, for that matter, the Marx Brothers — definitively demonstrated the physical possibilities of sound-era comedy.
Likewise, a decoy ODN designed to sequester activated CREB protein definitively demonstrated a requirement for CRE-mediated transcription in light signaling.
However, limited studies of humans who display sustained tolerance following transplantation have not definitively demonstrated a role for regulatory cells in this process.
Instead, the boats-for-regions comment seems, for a start, to have alarmed Turnbull, not least because it would have definitively demonstrated to him that Trump had not really been listening to, or understanding, a word he said.
The increased cardiovascular morbidity and mortality in severe PHPT has not been definitively demonstrated in mild disease, although there is some evidence for more subtle cardiovascular abnormalities, such as increased vascular stiffness, among others.
These findings definitively demonstrated the existence of interaction between TSG and emodin, which provide a basis for a better understanding of the underlying mechanism for PMR-induced liver injury.
Purpose: Treatment designed to eliminate thrombus in patients with iliofemoral deep venous thrombosis (DVT) is theoretically attractive; however, its benefits, compared with those of anticoagulation, have not been definitively demonstrated.
"To date, this has not been definitively demonstrated by any particular observation".
The 1992 observations of the COBE satellite definitively demonstrated that the shape was such a perfect blackbody that this alternative was ruled out.
More suggestions(15)
completely demonstrated
fully demonstrated
irrevocably demonstrated
certainly demonstrated
ultimately demonstrated
definitively designated
absolutely demonstrated
totally demonstrated
definitively substantiated
definitely demonstrated
decisively demonstrated
finally demonstrated
entirely demonstrated
definitively confirm this
definitively established by
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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