"substantiate their arguments" is a correct and usable phrase in written English.
It means to provide evidence or proof to support one's arguments. Example: The prosecutor was asked to substantiate their arguments with solid evidence in order to convince the jury of the defendant's guilt.
Justice Joan Madden said that the plaintiffs had failed to substantiate their argument that the demolition would "irrevocably harm the neighborhood," but that she was not judging the suit's merits.
The authors substantiate their argument in part through an analysis of experiments that led to a breakthrough discovery of weak neutral currents.
They cannot substantiate their argument.
The experts from the Van Gogh Museum said: "Truly nothing substantiates their argument for the train of events they construe, apart from a twentieth-century rumour arising from an authentic story of a trigger-happy brat in 1890, who merely claimed that Van Gogh probably stole the gun from him.
"The applicants had not substantiated their argument that people outside the UK were more likely to have their communications intercepted.
In the Mahabharata both sides present various arguments to substantiate their viewpoints.
Through meetings with Legislative Council members as well as officials in the Financial Services and Treasury Bureau, the coalition provided a variety of supporting arguments and figures to substantiate their case [ 38].
We studied which arguments Dutch physicians use to substantiate their adherence to the criteria and which aspects attract review committees' attention.
Advocates generate reams of numbers to substantiate their preferred outcome.
A number of witnesses provided time and date-stamped photographs which substantiated their accounts.
In support of their claim, they have submitted more than forty thousand pages of documentation substantiating their history and lineage.
