theorem Th2:
  m1 c= m2 & m2 c= m3 implies m1 c= m3
proof
  assume that
A1: m1 c= m2 and
A2: m2 c= m3;
  let p;
  assume
A3: p in P;
  then
A4: m1.p <= m2.p by A1;
  m2.p <= m3.p by A2,A3;
  hence thesis by A4,XXREAL_0:2;
end;
