∀ {R : Type u_5} {ι : Type u_1} {M₁ : ι → Type u_3} {M₂ : Type u_4} [inst : CommSemiring R]
  [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : AddCommMonoid M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
  [inst_4 : Module R M₂] {α : Type u_2} (f : MultilinearMap R M₁ M₂) {s : Set ι} (e : α ≃ ↑s)
  [inst_5 : DecidablePred fun x => x ∈ s] [inst_6 : DecidableEq { a // a ∉ s }] (m : (i : { a // a ∉ s }) → M₁ ↑i)
  (i : { a // a ∉ s }) (c : R) (x : M₁ ↑i),
  { toFun := fun v => ((f.domDomRestrictₗ fun i => i ∈ s) (Function.update m i (c • x))) fun i => v (e.symm i) ↑i,
      map_update_add' := ⋯, map_update_smul' := ⋯ } =
    c •
      { toFun := fun v => ((f.domDomRestrictₗ fun i => i ∈ s) (Function.update m i x)) fun i => v (e.symm i) ↑i,
        map_update_add' := ⋯, map_update_smul' := ⋯ }