Proof? What are they buying? How? It's obvious something is going on. But, WHAT are they buying or HOW are they doing this?
Inquiries into such activities can begin with the Plunge Protection Team (PPT) Working Group on Financial Markets. They have been using the futures markets to prop up the stock markets for some time, but there have been some concerns about the Obama Administration's role in making the PPT activities unprecedented and questionable.
See for one example:
http://www.abovetopsecret.com/forum/thread532757/pg1
The other means are much murkier and involve a wide variety of indirect approaches towards using TARP appropriations (GM, AIG, and so forrth), coordination with George Soros and others to make special deals that give the effect of federal monies leveraging third party investments in the markets.
The Fed reduces Goldman Sacks cash reserve requirement and in turn Goldman Sacks buys stocks and put them in inventory.