AGX's order-to-degree lower bound for the independence number

Let $G$ be a graph, let $\alpha(G)$ be its independence number, let $v$ be the number of vertices of $G$, and let $\Delta$ be its maximum degree. AGX's order-to-degree conjecture.

$$\alpha(G)\geq\frac{v-1}{\Delta}$$

The source attributes this bound to AGX conjecture-making software and verifies it for the graph classes considered there, but gives no general proof or disproof.