reserve p,q for Rational;
reserve g,m,m1,m2,n,n1,n2 for Nat;
reserve i,i1,i2,j,j1,j2 for Integer;
reserve R for Ring, F for Field;

theorem
for E being Field, F being strict Subfield of E holds E includes F
proof
let E be Field, F be strict Subfield of E;
the carrier of F c= the carrier of E
  & the addF of F = (the addF of E)||the carrier of F
  & the multF of F = (the multF of E)||the carrier of F
  & 1.E = 1.F & 0.E = 0.F by EC_PF_1:def 1;
then F is strict Subring of E by C0SP1:def 3;
then  ex T being strict Subring of E st T,F are_isomorphic;
hence thesis;
end;
