reserve i,j for Nat;
reserve i,j for Nat,
  x for variable,
  l for quasi-loci;
reserve C for initialized ConstructorSignature,
  c for constructor OperSymbol of C;
reserve a,a9 for quasi-adjective,
  t,t1,t2 for quasi-term,
  T for quasi-type,

  c for Element of Constructors;

theorem
 for t1,t2,t3 being expression of C st t1 matches_with t2 & t2 matches_with t3
  holds t1 matches_with t3
  proof
    let t1,t2,t3 be expression of C;
    given f1 being valuation of C such that
A1: t1 = t2 at f1;
    given f2 being valuation of C such that
A2: t2 = t3 at f2;
    take f2 at f1;
    thus thesis by A1,A2,ABCMIZ_1:149;
  end;
