
theorem
for F being Field,
    E being FieldExtension of F
for E1 being E-extending FieldExtension of F,
    E2 being E-extending FieldExtension of F
for h being Function of E1,E2 holds h is E-fixing implies h is F-fixing
proof
let F be Field, E be FieldExtension of F;
let E1 be E-extending FieldExtension of F,
    E2 be E-extending FieldExtension of F;
let h be Function of E1,E2;
assume AS: h is E-fixing;
now let a be Element of F;
  thus h.a = h.(@(a,E)) by FIELD_7:def 4
          .= @(a,E) by AS
          .= a by FIELD_7:def 4;
  end;
hence thesis;
end;
