"assertion for" is not a complete sentence and therefore it is not correct or usable in written English.
In a sentence, you can use the phrase "make an assertion for". For example, "The professor made an assertion for increased funding of the campus research project."
We may assert its existence, but we cannot support our assertion; for the only thing we could adduce in support of it would be the fact that the image was embodied or expressed.
Then she urged voters to fact-check her assertion for themselves.
The filmmakers substitute personal assertion for politics, as if Thatcher's voice itself had altered the behavior of millions.
My initial reaction was that this was a ridiculous assertion for which there is no hard evidence.
But Cohen insisted he did not lobby for his massive fees, an important assertion for the former lawyer since he never registered to lobby on their behalf.
It was a startling assertion for the leader of a communist country, where crackdowns on dissidents in the past had drawn sharp Vatican criticism.
It is a bold assertion for an enterprise that, for now, sponsors only three courses, which students can take as electives in a liberal arts program.
Among other things, an investigation would examine that assertion — for which Mr. Cheney offers no evidence, and which others have challenged.
Even a recreational fad becomes a form of self-assertion for a rising class or age group.
For all Minnie's cavalierly independent self-assertion, for all her apparently brave and admirable indifference to the way that her behavior is perceived, the movie itself is utterly disingenuous about Minnie's ingenuous bravado.
My son was a lively, intelligent, and very loveable boy until puberty; then he had various physical difficulties which appeared to give rise to a need for self-assertion, for he heroin addict: he lives longer, and consequently there is more hope of being able to cure him before it is too late.
