Definition subrr := addrN.Canonical add_monoid := Monoid.Law addrA add0r addr0.Canonical add_comoid := Monoid.ComLaw addrC.

(* Specifications: *)
Lemma addrCA : @left_commutative V V +%R.
Lemma addrAC : @right_commutative V V +%R.
Lemma addrACA : @interchange V +%R +%R.
Lemma addKr : @left_loop V V -%R +%R.
Lemma addNKr : @rev_left_loop V V -%R +%R.
Lemma addrK : @right_loop V V -%R +%R.
Lemma addrNK : @rev_right_loop V V -%R +%R.