theorem Th23:
  for k be Nat st k-equivalent qa, qb & k-equivalent qb, qc holds
  k-equivalent qa, qc
proof
  let k be Nat;
  assume that
A1: k-equivalent qa, qb and
A2: k-equivalent qb, qc;
  thus k-equivalent qa, qc
  proof
    let w be FinSequence of IAlph;
    assume
A3: len w <= k;
    then (qa, w)-response = (qb, w)-response by A1;
    hence thesis by A2,A3;
  end;
end;
