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

theorem
   for F being Field, p be Polynomial of F st deg p = 1 holds p splits_in F
   proof
     let F be Field;
     let p be Polynomial of F;
     assume deg p = 1; then
     consider x,z being Element of F such that
A1:  x <> 0.F & p = x * rpoly(1,z) by HURWITZ:28;
     reconsider x as non zero Element of F by A1,STRUCT_0:def 12;
     reconsider q = rpoly(1,z) as Ppoly of F by RING_5:51;
     p = x * q by A1;
     hence thesis;
   end;
