Section Matrix.
Variable (E : {subfield L}) (A : {set gal_of E}).
Let K := fixedField A.
End Matrix.

Lemma dim_fixed_galois K E (G : {group gal_of E}) :
galois K E -> G \subset 'Gal(E / K) ->
\dim_K (fixedField G) = #|'Gal(E / K) : G|.