Using "we have" in maths papers I commonly want to use the phrase "we have" when writing mathematics, to mean something like "most readers will know this thing and I am about to use it". My primary question is whether this is too colloquial. My secondary question is what the alternatives are if it is too colloquial.
For example, right now I have a sentence
"Given a point $P\in X$ we have the residue map ${\text {res}}_P \colon \Omega_{K(X)} \rightarrow k$, as defined in ...". I don't feel saying "there exists the" is quite right. Even if it is grammatically correct, I don't think this conveys the implication that it will be almost certainly familiar to the expected audience.
I have seen this question but I feel this is slightly different. If not then my apologies.

I would replace " we have" by ", then" or just ", " 
