∀ {R : Type u_1} [inst : CommRing R] [inst_1 : Algebra R ℝ] (g : Matrix.SpecialLinearGroup (Fin 2) R)
  (z : UpperHalfPlane),
  ↑(g • z) =
    (↑((algebraMap R ℝ) (↑g 0 0)) * ↑z + ↑((algebraMap R ℝ) (↑g 0 1))) /
      (↑((algebraMap R ℝ) (↑g 1 0)) * ↑z + ↑((algebraMap R ℝ) (↑g 1 1)))