theorem
  A c= dom f /\ dom g & f is A-measurable & g is A-measurable
  implies max-(f+g) + max+f is A-measurable
proof
  assume that
A1: A c= dom f /\ dom g and
A2: f is A-measurable and
A3: g is A-measurable;
A4: max+ f is A-measurable by A2,Th46;
A5: dom(f+g) = dom f /\ dom g by VALUED_1:def 1;
  f+g is A-measurable by A2,A3,Th26;
  then max-(f+g) is A-measurable by A1,A5,Th47;
  hence thesis by A4,Th26;
end;
