theorem Th39:
  for tfsm being finite non empty Mealy-FSM over IAlph, OAlph
  holds n+1 = card the carrier of tfsm implies final_states_partition tfsm = n
  -eq_states_partition tfsm
proof
  let tfsm be finite non empty Mealy-FSM over IAlph, OAlph;
  assume n+1 = card the carrier of tfsm;
  then (n+1)-eq_states_partition tfsm = n-eq_states_partition tfsm by Th35;
  then n-eq_states_partition tfsm is final by Th37;
  hence thesis by Def15;
end;
