reserve X1,x,y,z for set,
  n,m for Nat,
  X for non empty set;
reserve A,B for Event of Borel_Sets,
  D for Subset of REAL;
reserve Q for QM_Str;
reserve A1 for Element of Obs Q;
reserve s for Element of Sts Q;
reserve E for Event of Borel_Sets;
reserve ASeq for SetSequence of Borel_Sets;
reserve Q for Quantum_Mechanics;
reserve s for Element of Sts Q;
reserve x1 for Element of X1;
reserve Inv for Function of X1,X1;
reserve p,q,r,p1,q1 for Element of Prop Q;

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;
