∀ {ι : Type u_1} {R : Type u_3} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {v : ι → M} {x : M} (hli : LinearIndependent R v) (hsp : ⊤ ≤ Submodule.span R (Set.range v)),
  (Module.Basis.mk hli hsp).repr x = hli.repr ⟨x, ⋯⟩