intros.
unfold col, matXmat, matXvec in |- *.
simpl in |- *.
red in |- *; simpl in |- *.
intros.
apply sum_comp; auto with algebra.
Qed.
End facts.
Section morefacts.
From Algebra Require Export Cfield_facts.
Variable F : cfield.
Variable n m p : Nat.
Variable M : Mmn F m n.
Variable N : Mmn F n p.

Lemma matXmat_row :
forall i : fin m,
row (matXmat _ _ _ _ M N) i =' matXvec _ _ _ (transpose N) (row M i) in _.