Lets assume we have a semimartingale S and a martingale Z. In my lecture notes I have an equality I don't really understand
$$-\frac{1}{Z_t}d\langle S,Z\rangle_t = -d\langle S, \int_0^° \frac{dZ}{Z}\rangle _t$$
where $\langle , \rangle$ denotes the bounded variation and $d$ just the differential.
Can anyone explain to me what theorem or trick is used? It looks for me like the associativity of a stochastic integral but we have a bounded variation term and also no integral in front of the left side.
Thank you for your help!