I'am studying the book "Bott, Tu Differential forms in algebraic topology." I don't understand the proof of Leray-Hirsch theorem via Cech-de Rham complex.
Lets consider some bundle $\pi: E \mapsto M$ with fiber $F$ and some good open cover $\mathfrak{U}$ of the base $M$. There exist an isomorphism between cohomology of Cech-de Rham complex $C^*(\pi^{-1}\mathfrak{U}, \Omega^*)$ and $H^*(F) \otimes C^*(\mathfrak{U}, \Omega^*)$. Why?
