User:BigPansy/Sandbox

Proof of Stokes
Choose a finite family of coordinate systems $V_1,\dots,V_k$ on $X$ and a partition of unity $f_1,\dots,f_k$ with $f_1+\dots+f_k=1$ on $\mathrm{supp}\,\omega$ with $\mathrm{supp}\,f_i\subset V_i$ and $f_i$ compact.