Let $M$ be a compact smooth manifold, let $\pi: E \to M$ be a smooth real vector bundle of rank $k \in \mathbb{N}$, and let $C^\infty(M)$ denote the commutative ring of smooth real-valued functions on $M$. Then the $C^\infty(M)$-module $\Gamma(M,E)$ of smooth global sections of $E$ is finitely generated and projective.