 reserve K,F,E for Field,
         R,S for Ring;

theorem
   for S being RingExtension of R holds 1_.(S) = 1_.(R)
   proof
     let S be R-extending Ring;
     thus
     1_.(S) = 1.(Polynom-Ring S) by POLYNOM3:def 10
     .= 1.(Polynom-Ring R) by Th9
     .= 1_.(R) by POLYNOM3:def 10;
  end;
