
theorem ext0:
for F being Field,
    E being FieldExtension of F
for T1,T2 being Subset of E
st T1 c= T2 holds FAdj(F,T1) is Subfield of FAdj(F,T2)
proof
let F be Field, E be FieldExtension of F; let T1,T2 be Subset of E;
assume AS: T1 c= T2;
X: T2 is Subset of FAdj(F,T2) by FIELD_6:35;
now let o be object;
  assume o in T1;
  then o in T2 by AS;
  hence o in the carrier of FAdj(F,T2) by X;
  end; then
A: T1 c= the carrier of FAdj(F,T2);
F is Subfield of FAdj(F,T2) by FIELD_4:7;
hence FAdj(F,T1) is Subfield of FAdj(F,T2) by A,FIELD_6:37;
end;
