[Mike Haven]

i couldn't give mathematical proof, but here's a quick statement of logic, imo

if all players played all streets then they would all break even in the long run

if one player that wouldn't have won the pot folded before the end then the money needed for everyone to break even in the long run wouldn't be in the pot, and when he won his share in the long run he would win more money than he had put in

vice versa the others would not have won as much as they had put in