I have seen proof of [Tutte's theorem][1] from Gallai's lemma. Lovasz also said in his [Matching theory][2] 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
  [2]: http://books.google.com/books?id=yW3WSVq8ygcC&lpg=PA89&ots=a5O-f2opi2&dq=matching%2520theorem%2520gallai%2520lemma&pg=PA89#v=onepage&q&f=false
  [3]: http://i45.tinypic.com/2d98klw.png