Definition subrK := addrNK.

(* Specifications: *)
Lemma subKr x : involutive (fun y => x - y).
Lemma addrI : @right_injective V V V +%R.
Lemma addIr : @left_injective V V V +%R.
Lemma subrI : right_injective (fun x y => x - y).
Lemma subIr : left_injective (fun x y => x - y).
Lemma opprK : @involutive V -%R.
Lemma oppr_inj : @injective V V -%R.
Lemma oppr0 : -0 = 0 :> V.
Lemma subr0 x : x - 0 = x.
Lemma sub0r x : 0 - x = - x.
Lemma opprB x y : - (x - y) = y - x.
Lemma addrKA z x y : (x + z) - (z + y) = x - y.
Lemma subrKA z x y : (x - z) + (z + y) = x + y.
Lemma addr0_eq x y : x + y = 0 -> - x = y.
Lemma subr0_eq x y : x - y = 0 -> x = y.