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"firmly demonstrate" is correct and usable in written English and can be used to express certainty.
For example: The results of the experiment firmly demonstrate that the new material is stronger and more durable than previous materials.
Exact(10)
The results could firmly demonstrate the S-G filter's superiority.
Another limitation of our study is the absence of mechanistic studies that would more firmly demonstrate the crucial involvement of C5aR-activated intracellular pathways in septic encephalopathy.
Wodak added that what UNGASS will firmly demonstrate is "that the international drug policy consensus is irreparably broken".
However, most studies have been cross-sectional, precluding the ability to firmly demonstrate temporality of associations.
And previous epidemiological studies also firmly demonstrate that, with Lp(a) elevation, the risk for cardiovascular risk is significantly increased [ 22– 22].
The successful clinical applications of these TNF-α inhibitors firmly demonstrate the fact that TNF-α is indeed the key inflammatory mediator in RA.
Similar(50)
It also firmly demonstrates that Momentum is not to be a plaything of Loto.
Evidence that DNA acts as the carrier of the genetic information was first firmly demonstrated by exquisitely simple microbiological studies.
By voting for the two major parties opposed to this war, the Pakistani public has firmly demonstrated that it has no appetite for a US-sponsored military campaign.
Moreover, the critical importance of considering the local microenvironment in which different cells/tissues are naturally or experimentally engineered is firmly demonstrated.
Together, these findings were encouraging, as they firmly demonstrated that genetic design can be used to control monoterpene production and that the knowledge gained from our initial test set could guide subsequent design.
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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