# Normal bundle is locally trivial

Could someone tell me how to prove the following result?

Let $Z$ be a submanifold of codimension $k$ in $Y$. Prove that the normal bundle $N(Z;Y)=\left\{(z,v):z\in Z, v\in T_{z}(Y)\text{ and } v\bot T_{z}(Z)\right\}$ is locally trivial, that is, each point $z\in Z$ has a neighborhood $V$ in $Z$ such that $N(V;Y)$ is trivial.

Note: We say that the normal bundle $N(Z;Y)$ is trivial if there exists a diffeomorphism $\psi:N(Z;Y)\longrightarrow Z\times\mathbb{R}^k$ that restricts to a linear isomorphism $N_{z}(Z;Y)\longrightarrow\left\{z\right\}\times\mathbb{R}^k$ for each point $z\in Z$.

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