In game theory, the Nash Indifference Theorem states that if a mixed strategy $A$ is a best response to a mixed strategy $B$, then every pure strategy in the support of $A$ is also a best response to $B$ (with the same expected payoff).
I am looking for a written proof of this theorem that could be read by an undergraduate with a high school but not a college level math background. Are you aware of such a proof?
This document contains a proof (section 3, on pp. 18-19) but the sigma notation, double subscripts, and terse proof style will all be very hard for the students I have in mind.
I am not familiar with many standard texts in Game Theory; I'm hoping you may be aware of some that prove this theorem in a wordier and less notationally intense way.