reserve X, Y for non empty set;

theorem
  for R being RMembership_Func of X,X holds max(R,converse R) is symmetric
proof
  let R be RMembership_Func of X,X;
  set S = max(R,converse R);
  let x,y be Element of X;
  thus S.(x,y) = S. [x,y] .= max(R.(x,y), (converse R).(x,y)) by FUZZY_1:def 4
    .= max(R.(x,y), R.(y,x)) by FUZZY_4:26
    .= max((converse R).(y,x), R.(y,x)) by FUZZY_4:26
    .= S. [y,x] by FUZZY_1:def 4
    .= S.(y,x);
end;
