∀ (ι : Type u_1) [inst : Fintype ι] [inst_1 : DecidableEq ι] (A : Type u_3) [inst_2 : Semiring A] (M : Type u_2)
  [inst_3 : AddCommMonoid M] [inst_4 : Module A M] (f : Module.End A (ι → M)),
  (fun m => { toFun := fun x i => ∑ j, (m i j) (x j), map_add' := ⋯, map_smul' := ⋯ })
      ((fun f i j => { toFun := fun x => f (Pi.single j x) i, map_add' := ⋯, map_smul' := ⋯ }) f) =
    f