Proof. [#249] February 20, 2025 Matt Earnshaw The cartesian property of ϕ\phi ϕ gives us ϕ′=iϕ\phi ' = \frac {i}{\phi }ϕ′=ϕi for a unique globular cell i:p′→pi : p' \to pi:p′→p, and the cartesian property of ϕ′\phi 'ϕ′ gives us that ϕ=i−1ϕ′\phi = \frac {i^{-1}}{\phi '}ϕ=ϕ′i−1 for a unique globular cell j:p→p′j: p \to p'j:p→p′. With similar reasoning starting from ϕ′\phi 'ϕ′, we see that iii and jjj are inverses.