Consider three events (events as in the context of SR/GR) $A, B$, and $C$ where $A$ caused $B$ and $B$ causes $C$ $$A\rightarrow B\\ B\rightarrow C$$ It seems reasonable to say $$A\rightarrow C$$ but can we prove it mathematically?
The motivation of this question is to prove that no two causally disconnected events $D$ and $A$ can ever be connected via an indirect relation. That is if $$D\rightarrow E$$ then $$E\rightarrow A$$ is not possible since that would imply by transitivity of causality that $$D\rightarrow A$$
