A proof of a conjecture by Monin and Rana on equations defining $\bar{M}_{0,n}$

Monin and Rana conjectured a set of equations defining the image of the moduli space $\bar{M}_{0,n}$ under an embedding into $\mathbb{P}^1\times \cdots\times \mathbb{P}^{n-3}$ due to Keel and Tevelev and verified the conjecture for $n\leq 8$ using Macaulay2. We prove this conjecture for all $n$.