theorem Th1:
  K is Subfield of K
  proof
A1: the addF of K = (the addF of K) || the carrier of K by RELSET_1:19;
A2: the multF of K = (the multF of K) || the carrier of K by RELSET_1:19;
    the carrier of K c= the carrier of K & 1.K = 1.K & 0.K = 0.K;
    hence thesis by A1,A2,Def1;
  end;
