Trying to check $f: \mathbb{P}^1_A \rightarrow Spec(A)$ for separatedness (where $A$ denotes a com. Ring with one), I considered the map $\Delta_{\mathbb{P}^1_A / Spec(A)}: \mathbb{P}^1_A \rightarrow \mathbb{P}^1_A \times_{Spec(A)}\mathbb{P}^1_A$ and aksed myself whether the fibre product on the right hand side could be simplified.
Similar to the identity $Spec(B) \times_{Spec(A)} Spec(C) = B \otimes_AC$, is there a relation that can be applied?