reserve n,i,j,k for Nat;
reserve T for TuringStr,
  s for All-State of T;

theorem Th41:
  for s,t being TuringStr, x be State of t holds [ the AcceptS of
  s, x] in UnionSt(s,t)
proof
  let s,t be TuringStr,x be State of t;
  set p1=the AcceptS of s, B= [:{p1},the FStates of t :];
  reconsider p=p1 as Element of { p1 } by TARSKI:def 1;
  [ p, x] in B;
  hence thesis by XBOOLE_0:def 3;
end;
