Cartan’s magic formula

On a smooth manifold$M$, for any smooth vector field $X\in \mathfrak{X}(M)$ and a differential form $\alpha$, ${\mathcal{L}}_X\alpha =d{\iota }_X\alpha +{\iota }_{X}d\alpha$ Where ${\mathcal{L}}_X\alpha$ denotes the Lie derivative of $\alpha$ with respect to $X$, and ${\iota }_X$ denotes the interior product.

Proof

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