∀ {R : Type u_1} {A : Type u_4} {M : Type u_7} {N : Type u_8} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : Monoid M] [inst_4 : Monoid N] (e : M ≃* N) (m : M),
  (MonoidAlgebra.domCongr R A e).toLinearMap ∘ₗ MonoidAlgebra.lsingle m = MonoidAlgebra.lsingle (e m)