reserve m, n, i, k for Nat;
reserve IAlph, OAlph for non empty set,
  fsm for non empty FSM over IAlph,
  s for Element of IAlph,
  w, w1, w2 for FinSequence of IAlph,
  q, q9, q1, q2 for State of fsm;
reserve tfsm, tfsm1, tfsm2, tfsm3 for non empty Mealy-FSM over IAlph, OAlph,
  sfsm for non empty Moore-FSM over IAlph, OAlph,
  qs for State of sfsm,
  q, q1, q2 , q3, qa, qb, qc, qa9, qt, q1t, q2t for State of tfsm,
  q11, q12 for State of tfsm1,
  q21, q22 for State of tfsm2;
reserve OAlphf for finite non empty set,
  tfsmf for finite non empty Mealy-FSM over IAlph, OAlphf,
  sfsmf for finite non empty Moore-FSM over IAlph, OAlphf;

theorem Th33:
  Class (0-eq_states_EqR tfsm, q) = the carrier of tfsm
proof
  set 0e = 0-eq_states_EqR tfsm;
  set S = the carrier of tfsm;
  now
    let z be object;
    thus z in Class (0e, q) implies z in S;
    assume z in S;
    then reconsider z9 = z as Element of S;
    0-equivalent z9, q by Th25;
    then [z,q] in 0e by Def12;
    hence z in Class (0e, q) by EQREL_1:19;
  end;
  hence thesis by TARSKI:2;
end;
