Did they do the Nasty?

I think Hamlet and Ophelia did have sex because when hamlet is all wrapped up in his suicide at the end of his speech he says, "The fair Ophelia! Nymph, in thy orisons
Be all my sins remember'd." Hamlet is confessing that he has sinned against God with Ophelia. I think this strongly hints at them doing "it" Also in the line where Hamlet says, " but now the
time gives it proof. I did love you once." and Ophelia replies, "Indeed, my lord, you made me believe so." I think this also gives proof that they had sex because she had belived that he had loved her and in what other way is love better expressed!