theorem
  for M1, M2 being connected reduced finite non empty Mealy-FSM over
  IAlph, OAlph holds M1, M2-are_isomorphic iff M1, M2-are_equivalent
proof
  let M1, M2 be connected reduced finite non empty Mealy-FSM over IAlph,
  OAlph;
  thus M1, M2-are_isomorphic implies M1, M2-are_equivalent by Th63;
A1: M2, the_reduction_of M2-are_isomorphic by Th46;
  assume M1, M2-are_equivalent;
  then
A2: the_reduction_of M1, the_reduction_of M2-are_isomorphic by Th65;
  M1, the_reduction_of M1-are_isomorphic by Th46;
  then M1, the_reduction_of M2-are_isomorphic by A2,Th42;
  hence thesis by A1,Th42;
end;
