simpa [sq, mul_add, add_assoc, mul_assoc, one_add_one_eq_two, mul_left_comm y 2] using this.bit_zero
case neg
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 y : M
H' : Exponential x y
H : Exponential (2 * x + 1) (2 * y ^ 2)
IH : ∀ y_1 < 2 * (2 * y ^ 2), ∀ {x : M}, x < y_1 → (Exponential (x + 1) y_1 ↔ ∃ z ≤ y_1, y_1 = 2 * z ∧ Exponential x z)
hxy : 2 * x + 1 < 2 * (2 * y ^ 2)
left✝ : 2 * y ^ 2 ≤ 2 * (2 * y ^ 2)
ne1 : ¬y = 1
this✝¹ : y < y ^ 2
this✝ : Exponential (x + 1) (2 * y) ↔ ∃ z ≤ 2 * y, 2 * y = 2 * z ∧ Exponential x z
this : Exponential (x + 1) (2 * y)
⊢ Exponential (2 * x + 1 + 1) (2 * (2 * y ^ 2))
no goals