
theorem BE2:
for F being Field,
    E being FieldExtension of F,
    K being F-extending FieldExtension of E
for BE being non empty finite linearly-independent Subset of VecSp(E,F),
    BK being non empty finite linearly-independent Subset of VecSp(K,E)
holds card Base(BE,BK) = card BE * card BK
proof
let F be Field, E be FieldExtension of F,
    K be F-extending FieldExtension of E;
let BE be non empty finite linearly-independent Subset of VecSp(E,F),
    BK be non empty finite linearly-independent Subset of VecSp(K,E);
thus card BE * card BK = card [:BE,BK:] by CARD_2:46
                      .= card Base(BE,BK) by BE1;
end;
