The order bound conjecture for degree-$k+1$ vertices in minimal $k$-extendable bipartite graphs

Let $G$ be a minimal $k$-extendable bipartite graph, where $k\geqslant 1$, and let $n$ be its order. Let $V_{k+1}$ be the set of vertices of degree precisely $k+1$. Order bound conjecture.

$$|V_{k+1}|\geqslant \frac{n}{2}+2.$$

The authors state that this conjecture can be proved assuming the main conjecture, but no unconditional resolution is given in the supplied text.