No Need for Naps

Tyler does not like to take a nap. He fights me over taking a nap everyday. I've been told that he might be getting to old to need a nap anymore. I'm pretty sure that he still needs a nap & here's why:

Me: It's naptime.
Tyler: No! I don't want a nap! I'm not tired! I want to roller-skate outside! I want to play! I don't want a nap! I'm not tired! (And on and on.)
Me: Fine, just leave Claire alone so she can take a nap.
Tyler: OK, Mommy.

So, Tyler got his helmet & pads on and went outside to play. He got bored playing by himself & came in to wake Claire. I told him he'd be in trouble if he woke her. A few minutes later, I heard Claire screaming in her room. I went in there to find her sitting in her bed, holding her shoe. Apparently Tyler went in there, chucked her shoe at her and told her to put her shoes on & come outside to play. So, of course, Tyler was in trouble for waking her & throwing shoes at her. I sent him for time-out on the rug and I continued making dinner. About 15 minutes later, I realized that I forgot to tell him he could get off of the rug. When I went to tell him he could go play, this is what I found:

Wouldn't you say that looks like a boy who is not tired and does not need a nap?