reserve k,i for Nat;
reserve D for non empty set;

theorem
  for p being XFinSequence of D st NAT c= D &
  (p.0) is Nat & (p.0) in dom p holds p is_an_xrep_of (XFS2FS*(p))
proof
  let p be XFinSequence of D;
  assume that
A1: NAT c= D and
A2: (p.0) is Nat and
A3: (p.0) in dom p;
  reconsider m0=(p.0) as Nat by A2;
A4: m0<len p by A3,AFINSQ_1:86;
  (p.0) in len p by A3;
  then len (XFS2FS*(p)) =m0 & for i st 1<=i & i<= m0 holds (XFS2FS*(p)).i=p.i
  by AFINSQ_1:def 11;
  hence thesis by A1,A4;
end;
