theorem Th4:
  p |- q & q |- r implies p |- r
proof
  assume
A1: p |- q & q |- r;
  let s;
  Meas(p`1,s).p`2 <= Meas(q`1,s).q`2 & Meas(q`1,s).q`2 <= Meas(r`1,s).r`2
  by A1;
  hence thesis by XXREAL_0:2;
end;
