
theorem lemNor2ch:
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
holds h.:(the carrier of FAdj(F,T)) c= the carrier of FAdj(F,h.:T)
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;
let T be finite non empty F-algebraic Subset of E;
  h .: T is F-algebraic by ll; then
A0: FAdj(F,h.:T) = RAdj(F,h.:T) by help1;
now let o be object;
  assume o in h.:(the carrier of FAdj(F,T)); then
  consider a being object such that
  A1: a in dom h & a in the carrier of FAdj(F,T) & o = h.a by FUNCT_1:def 6;
  reconsider a as Element of FAdj(F,T) by A1;
  FAdj(F,T) = RAdj(F,T) by help1; then
  consider p being Polynomial of (card T),F,
           x being T-evaluating Function of (card T),E such that
  A2: a = Ext_eval(p,x) by help2;
  thus o in the carrier of FAdj(F,h.:T) by A0,A1,A2,help3;
  end;
hence thesis;
end;
