"support the assertion that" is correct and usable in written English.
You can use it when you want to demonstrate evidence for an assertion, or when you want to show that someone else's opinion agrees with your own assertion. Example: "Our research supports the assertion that climate change is real and needs to be addressed."
The age and gender differences observed are in keeping with previous literature and support the assertion that statin users represent a different patient group to those not using statin therapy.
These columns, too, hardly support the assertion that Medicare spending is out of control.
At this time, there is no evidence to support the assertion that CRRT improves clinical outcomes compared with IHD.
But what additional evidence exists to support the assertion that Abu Zubaydah was never with al-Qaida?
There is enough research evidence to support the assertion that it is not possible to regulate for mavericks.
They said the original study was "flawed" and did not support the assertion that having an abortion can make you mentally ill.
To support the assertion that drug plans will offer better value, Medicare officials said the average premium for drug coverage next year would be $24 a month.
He offered no evidence to support the assertion that the victims, who were not publicly identified, had been killed by guerrillas.
In what ways does the article support the assertion that carrots improve eyesight, and in what ways do they not have any effect?
There is, however, no evidence to support the assertion that these high rates are a consequence of psychiatrists misdiagnosing serious disorder at extraordinary levels in these populations.
Lewis also complains that the Sunday Times used several quotes from him in the piece to support the assertion that the IPCC report had made a false claim.
