 reserve x for Real,
    p,k,l,m,n,s,h,i,j,k1,t,t1 for Nat,
    X for Subset of REAL;
reserve x for object, X,Y,Z for set;
 reserve M,N for Cardinal;
reserve X for non empty set,
  s for sequence of X;

theorem
  s^\0 =s
proof
  now
    let n be Element of NAT;
    thus (s ^\0).n=s.(n+0) by Def2
      .=s.n;
  end;
  hence thesis by FUNCT_2:63;
end;
