
theorem subfie:
for F,K being Field holds K in SubFields F iff K is strict Subfield of F
proof
let F,K be Field;
now assume K in SubFields(F);
   then consider K1 being strict Field such that
   B: K1 = K & K1 is Subfield of F by defX;
   thus K is strict Subfield of F by B;
   end;
hence thesis by defX;
end;
