reserve i, i1, i2, j, k for Nat,
  r, s for Real;
reserve D for non empty set,
  f1 for FinSequence of D;

theorem Th23:
  for n being Nat,f being FinSequence holds
    S_Drop(n,f)=S_Drop(n+(len f-'1),f) &
      S_Drop(n,f)=S_Drop(len f-'1+n,f)
proof
  let n be Nat,f be FinSequence;
A1: (n+(len f-'1))mod (len f-'1) = (n+(len f-'1)*1)mod (len f-'1)
    .=n mod (len f-'1) by NAT_D:21;
  per cases;
  suppose
A2: n mod (len f-'1)<>0;
    then S_Drop(n,f)=n mod (len f-'1) by Def1;
    hence thesis by A1,A2,Def1;
  end;
  suppose
A3: n mod (len f-'1)=0;
    then S_Drop(n,f)=len f-'1 by Def1;
    hence thesis by A1,A3,Def1;
  end;
end;
