Theorem: LO.FirstOrder.Arith.Model.SPPow2.not_one (Arithmetization/ISigmaZero/Exponential/PPow2.lean)

State before:
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
m : M
hm : SPPow2 m
⊢ ¬SPPow2 1
Tactic:
rintro ⟨_, h, _⟩
State after:
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
m : M
hm : SPPow2 m
left✝ : ¬LenBit 1 1
h : LenBit 2 1
right✝ : ∀ i ≤ 1, Pow2 i → 2 < i → (LenBit i 1 ↔ (√i) ^ 2 = i ∧ LenBit (√i) 1)
⊢ False

State before:
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
m : M
hm : SPPow2 m
left✝ : ¬LenBit 1 1
h : LenBit 2 1
right✝ : ∀ i ≤ 1, Pow2 i → 2 < i → (LenBit i 1 ↔ (√i) ^ 2 = i ∧ LenBit (√i) 1)
⊢ False
Tactic:
simp [LenBit.iff_rem, one_lt_two] at h
State after:
no goals