I found this a most interesting problem, and I have now written out a formal proof. I assume that you have come up with one as well,
To tell the truth I tried… and failed…
but here's mine, if you're interested:
Of course I’m interested, I would love to see it.
Wow. That's awesome. I really appreciate your formal proof. Thanks for all the help.
I would be interested to see if you have found any significant way of shortening this proof.
I did not, but in like three months my teacher will make a proposal for a solution.