∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) {x y : V},
  ((Representation.Coinvariants.mk ρ) x = (Representation.Coinvariants.mk ρ) y) =
    (x - y ∈ Representation.Coinvariants.ker ρ)