If at the end of a proof, I showed the existence of some function with some properties that were to be proved, but in addition to that, some more structure to the function was revealed, how could I add a remark to state this?
For example, if it were an integral expression, and the integrand turned out to be odd, do I say this:
Remark: We observe that the integrand $f(x)$ is odd.
or, leave it alone and expect the reader to pick up on this extra structure?
I would like to state the one line remark, as I give a corollary that follows directly from the remark, but I am wary of stating something trivial.
It's always better to have more information rather than less. If you use the information, include it, else you should leave it alone.
A middle way could be "Since $f(x)$ is odd, ..."