
theorem lemNor2c:
for F being Field,
    E being FieldExtension of F,
    K being F-extending FieldExtension of E
for h being F-fixing Monomorphism of E,K
for T being non empty finite F-algebraic Subset of E
st h.:T c= the carrier of E
holds h.:(the carrier of FAdj(F,T)) c= the carrier of E
proof
let F be Field, E be FieldExtension of F,
    K be F-extending FieldExtension of E;
let h be F-fixing Monomorphism of E,K,
    T be non empty finite F-algebraic Subset of E;
assume h.:T c= the carrier of E; then
FAdj(F,h.:T) is Subfield of E by lemh; then
A: the carrier of FAdj(F,h.:T) c= the carrier of E by EC_PF_1:def 1;
h.:(the carrier of FAdj(F,T)) c= the carrier of FAdj(F,h.:T) by lemNor2ch;
hence thesis by A;
end;
