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

theorem
   for R being comRing, S being comRingExtension 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 R be comRing, S be comRingExtension of R;
     let a be Element of S;
     let p,q be Polynomial of R;
     R is Subring of S by Def1;
     hence thesis by ALGNUM_1:20;
  end;
