∀ {Γ : Subgroup (GL (Fin 2) ℝ)} [Γ.HasDetPlusMinusOne] (x : ℝ),
  ∀ g ∈ Γ,
    ∀ (τ : UpperHalfPlane),
      SlashAction.map 0 g (Function.const UpperHalfPlane ↑x) τ = Function.const UpperHalfPlane (↑x) τ