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

theorem Th8:
   S is RingExtension of R implies 0_.(S) = 0_.(R)
   proof
     assume
A1:  S is R-extending Ring;
     thus 0_.(S) = 0.(Polynom-Ring S) by POLYNOM3:def 10
     .= 0.(Polynom-Ring R) by A1,Th7
     .= 0_.(R) by POLYNOM3:def 10;
   end;
