https://www.maths.ed.ac.uk/~v1ranick/papers/botttu.pdf
I was reading chapter 14 of Bott & Tu. From p.161, the book discusses the spectral sequence of a double complex $K=\bigoplus_{p,q\geq 0} K^{p,q}$. At p.164, there is a conclusion that $d_r:E_r^{p,q}\to E_r^{p+r, q-r+1}$ is given by $d_r[b]_r=[\delta c_{r-1}]_r$. Then in (14.13), it is written that the successive quotients of the filtration of $H^n_D(K)$ are $E^{0,n}_\infty, \dots, E^{n,0}_\infty$. Why does this statement true? I think I understood the materials in the section before this statement, but I cannot see why this is true.. Am I missing something? Thanks in advance.