I think such proof is quite standard however I can't make them as the case of addition and multiplication functions. (which can be done by first prove $\mathsf{Q}\vdash x+/*y=z$ then show such $x +/*y = z$ represents addition/multiplication in Robinson's $\mathsf{Q}$).
However, I get stuck on the case of $/$ and $\%$, should they follow the same procedure?