110% Proof
Theorem: All natural numbers are equal.
Proof: It is sufficient to show that A=B for any two natural numbers.
Also, it is sufficient to show that for all N > 0, if A and B are two natural numbers that satisfy the rule [MAX(A, B) = N] then A = B.
Now, use mathematical induction.
First the anchor step: If N = 1, then A and B, being natural numbers, must both equal 1 by the rule. So A = B.
Now, assume that the claim is true for some value K, and we have to show it is true for K+1. Consider natural numbers A and B with MAX(A, B) = K+1. But then MAX((A1), (B1)) = K, implying that (A1) = (B1) or A = B.
QED!
