theorem Th57:
  for crq11, crq12 being State of CRtfsm1 holds crq11 = q1u &
  crq12 = q2u & the carrier of CRtfsm1 misses the carrier of CRtfsm2 & tfsm =
CRtfsm1-Mealy_union CRtfsm2 & not crq11, crq12-are_equivalent implies not q1u,
  q2u-are_equivalent
proof
  let crq11, crq12 be State of CRtfsm1;
  set rtfsm1 = CRtfsm1, rtfsm2 = CRtfsm2, q1 = crq11, q2 = crq12;
  assume that
A1: q1 = q1u and
A2: q2 = q2u and
A3: (the carrier of rtfsm1) misses (the carrier of rtfsm2) & tfsm =
  rtfsm1 -Mealy_union rtfsm2;
  assume not q1,q2-are_equivalent;
  then consider w be FinSequence of IAlph such that
A4: (q1,w)-response <> (q2,w)-response;
  (q1u,w)-response = (q1,w)-response by A1,A3,Th53;
  then (q1u,w)-response <> (q2u,w)-response by A2,A3,A4,Th53;
  hence thesis;
end;
