∀ {k : Type u_1} {G : Type u_3} {H : Type u_2} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : Monoid H] (φ : G →* H)
  (A : Rep.{max u_1 u_2, u_1, u_3} k G) (x : Rep.res φ (Rep.leftRegular k H) ⟶ A) (x_1 : H),
  ((Rep.Hom.hom
          ((fun f => Rep.ofHom { toLinearMap := Finsupp.linearCombination k ↑f, isIntertwining' := ⋯ })
            ((fun f => ⟨fun h => (Rep.Hom.hom f).toLinearMap fun₀ | h => 1, ⋯⟩) x))).toLinearMap
      fun₀ | x_1 => 1) =
    (Rep.Hom.hom x).toLinearMap fun₀ | x_1 => 1