∀ (R : Type u) [inst : CommRing R] {n : ℕ} {M : Type u_1} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Type u_4}
  [inst_3 : LinearOrder I] {v : I → M},
  Submodule.span R (Set.range v) = ⊤ → Submodule.span R (Set.range (exteriorPower.ιMulti_family R n v)) = ⊤