 reserve R for domRing;
 reserve p for odd prime Nat, m for positive Nat;
 reserve g for non zero Polynomial of INT.Ring;

theorem Th13:
  for i be Nat holds
  (Der1(INT.Ring)).(tau(i)) = 1.Polynom-Ring(INT.Ring)
   proof
     set D = Der1(INT.Ring);
     let i be Nat;
     len tau(i) = 2 by POLYNOM5:40; then
A2:  len (D.(tau i))
     = 2 - 1 by RING_3:76,E_TRANS1:17 .= 1;
     (D.(tau i)).0
     = (0+1)*((tau i).(0+1)) by RINGDER1:def 8
     .= <%In(-i,INT.Ring), 1.INT.Ring %>.1 by BINOM:13
     .= 1.INT.Ring by POLYNOM5:38; then
     D.(tau i) = <% 1.INT.Ring %> by A2,UPROOTS:19
     .= 1_.INT.Ring by UPROOTS:31
     .= 1.Polynom-Ring INT.Ring by POLYNOM3:def 10;
     hence thesis;
   end;
