∀ {k : Type u_3} {G : Type u_4} {V : Type u_1} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) (α : Type u_2) (x : G),
  Finsupp.mapRange.linearMap (Representation.Coinvariants.mk ρ) ∘ₗ (ρ.finsupp α) x =
    Finsupp.mapRange.linearMap (Representation.Coinvariants.mk ρ)