David Speyer wrote how I would say it in practise, in a context where I was writing it on a black/whiteboard. Here's how I would say it in a pub or walking down the street:
"Let's define a 'representation map for X' [or your own preferred jargon] to be just some partial function nu, from the natural numbers to X. Then we can define a computable sequence for that representation map nu to be any function s, from the natural numbers to X, which [is consistent with / agrees with / extends] the composition of nu with a computable function f on the natural numbers."
When using natural language, choose your nouns wisely and characterize them. Do you care about the ordered pair $(X,\nu_X)$, or really just the map $\nu_X$ (for which $X$ is just the background against which the idea is presented)? What is the role of the partial map $\nu_X$ in the idea you are communicating? Do you care about the integers $f(n) \in \mathop{\mathrm{dom}}(\nu_X)$ over which you quantify, or really just the domain of the composite function $\nu_X \circ f$?
Identify the main characters in the synopsis of your play, and their roles: you will have a better chance of transporting the objects and morphisms of your idea faithfully to your interlocutors.