no goals
R : Type u_2
inst✝⁴ : LinearOrderedCommRing R
M : Type u_3
inst✝³ : AddCommGroup M
inst✝² : Module R M
ι : Type u_1
inst✝¹ : Fintype ι
inst✝ : DecidableEq ι
e : Basis ι R M
f : M ≃ₗ[R] M
⊢ Basis.orientation (Basis.map e f) = Basis.orientation e ↔ 0 < ↑LinearMap.det ↑f
rw [orientation_map, e.map_orientation_eq_det_inv_smul, units_inv_smul, units_smul_eq_self_iff,
  LinearEquiv.coe_det]