I have seen proof of [Tutte's theorem][1] from Gallai's lemma. Lovasz also said in his Matching theory that Gallai's lemma can be easily proven from Tutte's theorem. But I cannot figure out how. 

![alt text][3]
Thanks!


  [1]: http://en.wikipedia.org/wiki/Tutte_theorem
  [3]: http://i45.tinypic.com/2d98klw.png