∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (motive : (∃ s, Finsupp.linearCombination R id ∘ₗ s = LinearMap.id) → Prop)
  (x : ∃ s, Finsupp.linearCombination R id ∘ₗ s = LinearMap.id),
  (∀ (e : M →ₗ[R] M →₀ R) (he : Finsupp.linearCombination R id ∘ₗ e = LinearMap.id), motive ⋯) → motive x