red in |- *.
simpl in |- *.
auto.
Qed.
Definition row (F : field) :
forall m n : Nat, matrix F m n -> fin m -> Fn F n :=
fun n m M i => Ap2_Map M i.
Definition col (F : field) :
forall m n : Nat, matrix F m n -> fin n -> Fn F m :=
fun n m M j => Ap2_Map' M j.

Lemma row_transpose_col :
forall (F : field) (m n : Nat) (M : matrix F m n) (i : fin m),
row M i =' col (transpose M) i in _.