theorem Th12:
  f is_integrable_on M & g is_integrable_on M implies f-g is_integrable_on M
proof
  assume that
A1: f is_integrable_on M and
A2: g is_integrable_on M;
  (-jj)(#)g is_integrable_on M by A2,MESFUNC5:110;
  then -g is_integrable_on M by MESFUNC2:9;
  then f+(-g) is_integrable_on M by A1,MESFUNC5:108;
  hence thesis by MESFUNC2:8;
end;
