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 Lm1:
  for E being Field, F being Subfield of E holds F is Subring of E
  proof
    let E be Field, F be 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;
    hence F is Subring of E by C0SP1:def 3;
  end;
