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;
reserve tfsm, rtfsm for finite non empty Mealy-FSM over IAlph, OAlph,
  q for State of tfsm;
reserve qr1, qr2 for State of rtfsm,
  Tf for Function of the carrier of tfsm1, the carrier of tfsm2;
reserve Rtfsm for reduced finite non empty Mealy-FSM over IAlph, OAlph;
reserve Ctfsm, Ctfsm1, Ctfsm2 for connected finite non empty Mealy-FSM over
  IAlph, OAlph;

theorem Th48:
  accessibleStates tfsm c= the carrier of tfsm & for q holds q in
  accessibleStates tfsm iff q is accessible
proof
  set AS = { q where q is State of tfsm: q is accessible };
  AS c= the carrier of tfsm
  proof
    let x be object;
    assume x in AS;
    then ex q being State of tfsm st x = q & q is accessible;
    hence thesis;
  end;
  hence accessibleStates tfsm c= the carrier of tfsm;
  let q be State of tfsm;
  hereby
    assume q in accessibleStates tfsm;
    then ex q9 being State of tfsm st q9 = q & q9 is accessible;
    hence q is accessible;
  end;
  thus thesis;
end;
