simp [one_add_one_eq_two, two_mul_two_eq_four]
case pos.refl
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
IH : ∀ y < 2 * (2 * 1 ^ 2), ∀ {x : M}, x < y → (Exponential (x + 1) y ↔ ∃ z ≤ y, y = 2 * z ∧ Exponential x z)
left✝ : 2 * 1 ^ 2 ≤ 2 * (2 * 1 ^ 2)
H' : Exponential 0 1
H : Exponential (2 * 0 + 1) (2 * 1 ^ 2)
hxy : 2 * 0 + 1 < 2 * (2 * 1 ^ 2)
⊢ Exponential (2 * 0 + 1 + 1) (2 * (2 * 1 ^ 2))
no goals