reserve X for set;

theorem
  for S being Field_Subset of X, M being Measure of S,
      A being Element of S, B being measure_zero of M st A c= B holds
    A is measure_zero of M
proof
  let S be Field_Subset of X, M be Measure of S, A be Element of S, B be
  measure_zero of M;
  assume A c= B;
  then M.A <= M.B by Th8;
  then
A1: M.A <= 0. by Def4;
  0.<= M.A by Def2;
  then M.A = 0.by A1;
  hence thesis by Def4;
end;
