let X be non empty TopSpace; :: thesis: for x being Point of X st Cl {x} = {x} holds
{x} is maximal_anti-discrete
let x be Point of X; :: thesis: ( Cl {x} = {x} implies {x} is maximal_anti-discrete )
assume Cl {x} = {x} ; :: thesis: {x} is maximal_anti-discrete
then ( {x} is closed & {x} is anti-discrete ) by Th8;
hence {x} is maximal_anti-discrete by Th19; :: thesis: verum