I have a set $S(k)$ well defined only if $k>0$, and another set $X$ well defined only if a condition $cond$ is satisfied.
I want to define $S(k)$ as the union of $S(k-1)$ and $X$ provided that both are well defined. How can I express this ?
If I write $S(k) = S(k-1) \cup X$, this is not correct if $k=1$ or $cond$ is false.
Thank you.