The phrase "asserting against" is correct and usable in written English.
It can be used in contexts where someone is making a claim or statement that opposes or challenges something or someone.
Example: "The lawyer is asserting against the validity of the contract in court."
Alternatives: "claiming against" or "contesting against".
For a few years the supporters of Novatian had been active in Africa, asserting against Cyprian that no forgiveness for lapsed Christians was possible.
Update 3: The Foss Patents blog has obtained a full list of the 24 patents Ericsson is asserting against Samsung.
(A full list of the 24 wireless standards-essential patents Ericsson was asserting against Samsung in this specific dispute can be found here, on the FOSS Patents blog).
Blow opted to present his story through on-screen text instead of in-game cutscenes, asserting, against criticism of the lack of such cut-scenes, that Braid was "conceived as a videogame with its story presented in the tradition of a few books that I respect".
The "liberty of conscience", so important to Enlightenment thinkers in general, and asserted against all manner of paternalistic authorities (including Protestant), descends from this Protestant assertion.
"It is not easy to stand by as false allegations are asserted against the firm".
"They wanted to buy something that they could use to assert against someone else," he wrote in one.
"It is not easy to stand by as false allegations are asserted against the firm," he wrote.
It holds that borrowers' legal claims against their lenders can also be asserted against any subsequent purchasers of the loans.
At some point even the most dedicated numbers fanatic would accept that quality has to be asserted against quantity.
The jury also found that all the patent infringement claims that GlaxoSmithKline asserted against Genentech were invalid.
