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

theorem Th39:
  for t1,t2 being TuringStr holds [ the InitS of t1, the InitS of
t2 ] in UnionSt(t1,t2) & [ the AcceptS of t1,the AcceptS of t2 ] in UnionSt(t1,
  t2)
proof
  let t1,t2 be TuringStr;
  set p0=the InitS of t1, q0=the InitS of t2, p1=the AcceptS of t1, q1=the
AcceptS of t2, A= [: the FStates of t1, { q0 } :],
   B= [: {p1}, the FStates
of t2
  :];
  reconsider q=q0 as Element of { q0 } by TARSKI:def 1;
  reconsider p=p1 as Element of { p1 } by TARSKI:def 1;
  [ p0, q ] in A;
  hence [ p0, q0 ] in UnionSt(t1,t2) by XBOOLE_0:def 3;
  [ p, q1 ] in B;
  hence thesis by XBOOLE_0:def 3;
end;
