exact ⟨z, by simpa using hz⟩
case intro.intro
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀
x z : M
hz : Exponential x z
this : x < 2 * z → (Exponential (x + 1) (2 * z) ↔ ∃ z_1 ≤ 2 * z, 2 * z = 2 * z_1 ∧ Exponential x z_1)
hxy : x < 2 * z
⊢ ∃ z_1 ≤ 2 * z, 2 * z = 2 * z_1 ∧ Exponential x z_1
no goals