reserve x,y for Real,
  i, j for non zero Element of NAT,
  I, O for non empty set,
  s,s1,s2,s3 for Element of I,
  w, w1, w2 for FinSequence of I,
  t for Element of O,
  S for non empty FSM over I,
  q, q1 for State of S;

theorem
  q is accessible & q <> the InitS of S implies ex s st q is_accessible_via s
proof
  assume that
A1: q is accessible and
A2: q <> the InitS of S;
  consider W be FinSequence of I such that
A3: the InitS of S,W-leads_to q by A1;
  W <> {}
  by FSM_1:def 2,A2,A3;
  then consider S being Element of I, w9 being FinSequence of I such that
  W.1 = S and
A4: W = <*S*>^w9 by FINSEQ_3:102;
  take S;
  thus thesis by A3,A4;
end;
