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Will I be able to trade in F&O with Equity sale proceeds?

As per the exchange settlement cycle for equity is T+2. This implies that if you sell equity, the sales proceeds will be realized on the T+2 day.

For F&O, all brokers are required to report on a daily basis details in respect of the margin amount due and collected from the clients, with respect to the trades executed/open positions of the clients. 

For the purpose of margin reporting, sales proceeds which are not realised will be considered equivalent to collateral margins until realised. So, when opening new F&O positions, the margin reported will be, the value of sale proceeds minus haircut. The haircut % can be found in NSE F&O list of approved scrips as collateral

Let's understand this with an example,

Assume you have 0 balance in your trading account and you sold 100 shares of Infosys from your holdings at ₹1300, the sale proceeds would be ₹1,30,000. You will receive this amount 2 days later. Now on the same day, you buy 2 lots of NIFTY FUT which costs ₹1,25,000. The haircut % on Infosys shares is 12.5%.

So while reporting Margins for your NIFTY FUT position, we will report ₹1,13,750 (1,30,000 - 12.5%). So, in this case, there will be a margin shortfall of ₹ 11,250, on which you'll be charged penalty by the exchange.

However, you will be able to use these sales proceeds to buy Equity (delivery) and also trade intraday, since there is no concept of margin reporting in the Equity cash segment.