All 4 Uses

assert
in
Flags of Our Fathers
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Months before, a Marine officer had summed up the Navy's attitude when he pointed a finger at his Navy counterparts and asserted, "Even though you Navy officers do come in to about one thousand yards, I remind you that you have a little more armor.†
Chpt 6.
In Weslaco, Belle Block remained unconvinced by this assertion.†
Chpt 15.
A commentator on the NBC Blue network baldly asserted that the image had been "carefully posed" by Joe.†
Chpt 15. *
The assertion was later retracted, and the photographer tried to take it in stride.†
Chpt 15.

Definitions:

(1) (assert as in: asserted her opinion that...)
to say that something is true -- especially something disputed
(2) (assert as in: asserted her authority)
to be forceful in exercising influence or rights
(3) (meaning too rare to warrant focus)