intros.
simpl in |- *.
red in |- *; simpl in |- *.
intros.
destruct M; destruct M'; simpl in |- *.
simpl in H.
apply Trans with (Ap2 i' x); auto with algebra.
Qed.

(* Specifications: *)
Lemma col_comp :
forall (F : field) (m n : Nat) (M M' : matrix F m n) (i i' : fin n),
M =' M' in _ -> i =' i' in _ -> col M i =' col M' i' in _.