∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {ι : Type u_1}
  [inst_3 : Nonempty ι] [inst_4 : Fintype ι] {b : ι → V} (lin_ind : LinearIndependent K b)
  (card_eq : Fintype.card ι = Module.finrank K V) (a : V),
  (basisOfLinearIndependentOfCardEqFinrank lin_ind card_eq).repr a =
    lin_ind.repr ((LinearMap.codRestrict (Submodule.span K (Set.range b)) LinearMap.id ⋯) a)