wilmott.com

Has anybody proved this delta hedging day pnl = 0.5(realized_volatity - implied_volatility)gamma x S^2 x dt in a spreadsheet. 
I reconciled option price change = delta here 

I don't know how much correct this is

What do you mean proved this? One of the classic papers on this topic is "which free lunch would you like today, sir", by Wilmott and Ahmad. Google it.

reconciled formula