I am asking for a reference that contains a proof of Theorem 4, which is on page 315 of the following text:

Hirsch, Morris W., and Stephen Smale.

Differential equations, dynamical systems, and linear algebra. Vol. 60. Academic press, 1974.

Let $W$ be an open set in a vector space and $\mathcal{V}(W)$ be the set of all $C^1$ vector fields on $W$. Let $D^n = \{ x \in \mathbb{R}^n : \lvert x \rvert \leq 1 \}$. Consider in $\mathcal{V}(D^n)$ the set $\mathrm{grad}(D^n)$ of gradient vector fields that point inward on $D^n$.

**Theorem 4** *The set of structurally stable systems contained in $\mathrm{grad}(D^n)$ is open and dense in $\mathrm{grad}(D^n)$.*