Proof.  [#249]

The cartesian property of $\phi$ gives us $\phi ' = \frac {i}{\phi }$ for a unique globular cell $i : p' \to p$, and the cartesian property of $\phi '$ gives us that $\phi = \frac {i^{-1}}{\phi '}$ for a unique globular cell $j: p \to p'$. With similar reasoning starting from $\phi '$, we see that $i$ and $j$ are inverses.