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

theorem
   for S being RingExtension of R,a being Element of S,
   p,q being Polynomial of R holds
   Ext_eval(p+q,a) = Ext_eval(p,a) + Ext_eval(q,a)
   proof
     let S be RingExtension of R, a be Element of S;
     let p,q be Polynomial of R;
     R is Subring of S by Def1;
     hence thesis by ALGNUM_1:15;
   end;
