reserve X for set;

theorem Th10:
  for S being Field_Subset of X, M being Measure of S,
      A,B being Element of S holds M.(A \/ B) <= M.A + M.B
proof
  let S be Field_Subset of X, M be Measure of S, A,B be Element of S;
  set C = B \ A;
A1: A misses C by XBOOLE_1:79;
A2: M.C <= M.B by Th8,XBOOLE_1:36;
  M.(A \/ B) = M.(A \/ C) by XBOOLE_1:39
    .= M.A + M.C by A1,Def3;
  hence thesis by A2,XXREAL_3:36;
end;
