∀ (A : Type u_1) {K : Type u_2} {L : Type u} {B : Type u_4} [inst : CommRing A] [inst_1 : Field K] [inst_2 : CommRing B]
  [inst_3 : Field L] [inst_4 : Algebra A K] [inst_5 : Algebra B L] [inst_6 : Algebra A B] [inst_7 : Algebra K L]
  [inst_8 : Algebra A L] [inst_9 : IsScalarTower A K L] [inst_10 : IsScalarTower A B L]
  [inst_11 : FiniteDimensional K L] [inst_12 : Algebra.IsSeparable K L] (I : Submodule B L) {ι : Type u_3}
  [inst_13 : Finite ι] [inst_14 : DecidableEq ι] (b : Module.Basis ι K L),
  Submodule.restrictScalars A I = Submodule.span A (Set.range ⇑b) →
    Submodule.restrictScalars A (Submodule.traceDual A K I) = Submodule.span A (Set.range ⇑b.traceDual)