reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;
reserve i for Nat;
reserve m for Nat,
        D for non empty set;

theorem
  for p being XFinSequence of D st p.0=0 & 0<len p holds
  XFS2FS*(p)={}
proof
  let p be XFinSequence of D;
  assume that
A1: p.0=0 and
A2: 0<len p;
  set q= XFS2FS*(p);
  0 in len p by A2,Lm1;
  then len q=0 by A1,Def11;
  hence thesis;
end;
