The principal ideal theorem dimension conjecture for differential domains

Let $(K,\partial)$ be a differential field of characteristic zero. Let $A$ be a differentially finitely generated differential $K$-domain, let $f\in A$ be a non-unit, and let $P$ be a minimal prime ideal over the differential ideal $[f]$. PIT Dimension Conjecture. Then

$$\operatorname{trdeg}^{\partial}_K(A/P)\geq \operatorname{trdeg}^{\partial}_K(A)-1.$$

This is the differential analogue of Krull's principal ideal theorem and is the formulation used for inductive arguments in the paper. The source states that it is equivalent to Cohn's and Ritt's Dimension Conjectures, which remain open.