
theorem simp2:
for F being Field
for E being FieldExtension of F
for K being F-extending FieldExtension of E
holds IntermediateFields(E,F) c= IntermediateFields(K,F)
proof
let F be Field, E be FieldExtension of F, K be F-extending FieldExtension of E;
now let o be object;
  assume o in IntermediateFields(E,F); then
  consider U being strict Field such that
  A: U = o & F is Subfield of U & U is Subfield of E by defY;
  E is Subfield of K by FIELD_4:7; then
  U is Subfield of K by A,EC_PF_1:5;
  hence o in IntermediateFields(K,F) by A,defY;
  end;
hence thesis;
end;
