Proof of Proposition 2 in Ch.7 Spivak Vol.2: n-Dimensional Distribution?

[joe2317]

Hi.

I have a question on proof of proposition 2 in chater 7 Spivak volume2.
In the proof, he says that the n-dimensional distribution
$$\Delta_{p}$$=$$\bigcap^{n}_{i,j=1}$$ker$$\Lambda^{i}_{j}$$(p)
in R^(n+n^2) is integrable.
Could anyone explain why it is an n dimensional distribution?
Thanks.

 

[joe2317]

Never mind. I figured this out.