Fact oppmx_key : unit.Fact addmx_key : unit.Definition oppmx A := \matrix[oppmx_key]_(i, j) (- A i j).Definition addmx A B := \matrix[addmx_key]_(i, j) (A i j + B i j).

(* Specifications: *)
Lemma addmxA : associative addmx.
Lemma addmxC : commutative addmx.
Lemma add0mx : left_id (const_mx 0) addmx.
Lemma addNmx : left_inverse (const_mx 0) oppmx addmx.