theorem Th32:
  for tfsm being finite non empty Mealy-FSM over IAlph, OAlph
  holds k-eq_states_partition tfsm = (k+1)-eq_states_partition tfsm or card (k
  -eq_states_partition tfsm) < card ((k+1)-eq_states_partition tfsm)
proof
  let tfsm be finite non empty Mealy-FSM over IAlph, OAlph;
  set kp = k-eq_states_partition tfsm;
  set k1p = (k+1)-eq_states_partition tfsm;
  card kp <= card k1p by Th28,FINSEQ_4:89;
  then
A1: card kp = card k1p or card kp < card k1p by XXREAL_0:1;
  assume kp <> k1p;
  hence thesis by A1,Th28,FINSEQ_4:91;
end;
