reserve Y for non empty set;
reserve B for Subset of Y;

theorem Th8:
  for a being Function of Y,BOOLEAN holds a 'or' O_el(Y)=a
proof
  let a be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'or' O_el(Y)).x = a.x 'or' O_el(Y).x by Def4
    .= a.x 'or' FALSE by Def10
    .= a.x;
end;
