theorem
 for A1,A2,A3 being Subset of QuasiAdjs C
  st A1 matches_with A2 & A2 matches_with A3
  holds A1 matches_with A3
  proof
    let t1,t2,t3 be Subset of QuasiAdjs C;
    given f1 being valuation of C such that
A1: t2 at f1 c= t1;
    given f2 being valuation of C such that
A2: t3 at f2 c= t2;
    take f2 at f1;
    (t3 at f2) at f1 c= t2 at f1 by A2,ABCMIZ_1:146; then
    (t3 at f2) at f1 c= t1 by A1;
    hence thesis by ABCMIZ_1:150;
  end;
