reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;
reserve D for non empty set,
  F,G for XFinSequence of D,
  b for BinOp of D,
  d,d1,d2 for Element of D;
reserve F for XFinSequence,
        rF,rF1,rF2 for real-valued XFinSequence,
        r for Real,
        cF,cF1,cF2 for complex-valued XFinSequence,
        c,c1,c2 for Complex;
reserve r,s for XFinSequence;

theorem
  for D being set, p being one-to-one XFinSequence of D, n being Nat
  holds rng(p|n) misses rng(p/^n)
proof
  let D be set, p be one-to-one XFinSequence of D, n be Nat;
  rng((XFS2FS p)|n) misses rng((XFS2FS p)/^n) by FINSEQ_5:34;
  then rng((XFS2FS p)|n) misses rng(XFS2FS(p/^n)) by Th17;
  then rng(XFS2FS(p|n)) misses rng(XFS2FS(p/^n)) by Th17;
  then rng(XFS2FS(p|n)) misses rng(p/^n) by AFINSQ_1:97;
  hence rng(p|n) misses rng(p/^n) by AFINSQ_1:97;
end;
