In reading Rathjen (Choice principles in constructive set theories) and Jager (On Feferman's OST) I've come across two facts that are taken as obvious/well known, and probably are, but for which I cannot find a reference/work out how to prove. Either a reference or even just a hint in the right direction of how they might be shown would be much appreciated!!
The two facts are very similar:
1) $KP + V = L$ is conservative over $KP$ for $\Sigma_1$ formulae (Rathjen,p10)
2) $KP + V = L$ is conservative over $KP$ for absolute formulae (Jager, p30)
*in both cases the axiom of infinity is assumed.
As I say even just a general proof strategy for working out such claims would be much (perhaps more) appreciated.