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

theorem
   K is Subfield of K
   proof
A1:  the addF of K = (the addF of K) || the carrier of K;
A2:  the multF of K = (the multF of K) || the carrier of K;
     the carrier of K c= the carrier of K & 1.K = 1.K & 0.K = 0.K;
     hence thesis by A1,A2,EC_PF_1:def 1;
   end;
