reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;
reserve s for Element of D*;

theorem
  for z being Tuple of i+1,D ex t being Element of i-tuples_on D, d
   st z = t^<*d*>
proof
  let z be Tuple of i+1,D;
  consider t being Element of i-tuples_on D, s being Element of 1-tuples_on D
   such that
A1: z = t^s by Th104;
  ex d st s = <*d*> by Th95;
  hence thesis by A1;
end;
