∀ {n : Type u} {R : Type v} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing R] [inst_3 : LinearOrder R]
  [inst_4 : IsStrictOrderedRing R] (A : GL n R), A ∈ Matrix.GLPos n R ↔ 0 < ↑(Matrix.GeneralLinearGroup.det A)