theorem
  q1, q2-are_equivalent & q2, q3-are_equivalent implies q1, q3 -are_equivalent
proof
  assume that
A1: q1, q2-are_equivalent and
A2: q2, q3-are_equivalent;
  thus q1, q3-are_equivalent
  proof
    let w be FinSequence of IAlph;
    (q1, w)-response = (q2, w)-response by A1;
    hence thesis by A2;
  end;
end;
