reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem Th33:
  for f being FinSequence holds rng(f/^n) c= rng f
proof
  let f be FinSequence;
  let p be object;
  assume p in rng(f/^n);
  then consider j being object such that
A1: j in dom(f/^n) and
A2: (f/^n).j = p by FUNCT_1:def 3;
  reconsider jj = j as Nat by A1;
  jj+n in dom f by A1,Th26;
  then f.(jj+n) in rng f by FUNCT_1:def 3;
  hence thesis by A1,A2,Th27;
end;
