Proof.  [#249]

The cartesian property of ϕ\phi gives us ϕ=iϕ\phi ' = \frac {i}{\phi } for a unique globular cell i:ppi : p' \to p, and the cartesian property of ϕ\phi ' gives us that ϕ=i1ϕ\phi = \frac {i^{-1}}{\phi '} for a unique globular cell j:ppj: p \to p'. With similar reasoning starting from ϕ\phi ', we see that ii and jj are inverses.