∀ {R : Type u_1} (A : Type u_3) {ι : Type u_5} {M : Type u_6} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : AddCommMonoid M] [inst_3 : Algebra R A] [inst_4 : Module A M] [inst_5 : Module R M]
  [inst_6 : IsScalarTower R A M] (b : Module.Basis ι R M) (h : Function.Bijective ⇑(algebraMap R A)) (a : M) (a_1 : ι),
  ((Module.Basis.algebraMapCoeffs A b h).repr a) a_1 = (algebraMap R A) ((b.repr a) a_1)