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



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> Hirsch, Morris W., and Stephen Smale.
>  *Differential equations, dynamical systems, and linear algebra*. Vol. 60.
>  Academic press, 1974.
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> 
> 


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 $\mathrm{grad}(D^n)$.*



Reference Request: Structural Stability of Gradient Fields
This came out of J. Palis' 1967 Thesis:


J. Palis "On Morse-Smale dynamical systems" Topology 8, 1969, 385--405.


But that dealt with dimension $\leq 3$. The result you mention seems to first appear as a corollary in



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> J. Palis and S. Smale "Structural stability theorems" in Global analysis proceedings Symp. Pure Math., 14 AMS, 1970, 223--231.
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