Nice video! The binary representation and its xor op took the same teaching time to the theorem proof. I think if we should shorten the former or prolong the latter. For the last part of the proof, we can do one intermediate step to help understand: a' xor b xor c = a' xor (a xor a) xor b xor c = (a' xor a) xor (a xor b xor c) = (0...1rrrrr) xor (0...1rrrrr) = 0. The induction hypothesis should be emphasized (seems mentioned only one time), I felt that the proof assumes the theorem is correct, actually the proof (k+1) assumes (1 to k) are correct.
