Section Simmxity.
Context {F : fieldType}.
End Simmx.
End Simmxity.

Lemma diagonalizable_for_sum (F : fieldType) (m n : nat) (p_ : 'I_n -> nat)
(V_ : forall i, 'M[F]_(p_ i, m)) (A : 'M[F]_m) :
mxdirect (\sum_i <<V_ i>>) ->
(forall i, stablemx (V_ i) A) ->
(forall i, row_free (V_ i)) ->
diagonalizable_for (\mxcol_i V_ i) A = [forall i, diagonalizable_for (V_ i) A].