constructor
⊢ (∀ ⦃a₁ a₂ : ℝ⦄, bij_fun a₁ = bij_fun a₂ → a₁ = a₂) ∧
    ∀ (a : ℝ) (b : a > Real.sqrt 2), ∃ a_1, bij_fun a_1 = { val := a, property := b }
case left

⊢ ∀ ⦃a₁ a₂ : ℝ⦄, bij_fun a₁ = bij_fun a₂ → a₁ = a₂

case right

⊢ ∀ (a : ℝ) (b : a > Real.sqrt 2), ∃ a_1, bij_fun a_1 = { val := a, property := b }