theorem Th5: :: from BALLOT_1:5
  for D being set
  for d be FinSequence of D holds XFS2FS (FS2XFS d) = d
proof
  let D be set;
  let d be FinSequence of D;
  set Xd=FS2XFS d;
A1: len d = len Xd by AFINSQ_1:def 8;
A2: len Xd = len XFS2FS Xd by AFINSQ_1:def 9;
  now let i such that
A3: 1 <= i and
A4: i <= len d;
    reconsider i1=i-1 as Nat by A3,NAT_1:21;
A5: i1+1 = i;
    thus d.i = Xd.i1 by A4,A5,NAT_1:13,AFINSQ_1:def 8
            .= (XFS2FS Xd).i by A3,A4,A1,AFINSQ_1:def 9;
  end;
  hence thesis by A1,A2;
end;
