Theorem: LO.FirstOrder.Arith.Model.Pow2.not_three (Arithmetization/ISigmaZero/Exponential/Pow2.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
⊢ ¬Pow2 3
Tactic:
intro h
State after:
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
h : Pow2 3
⊢ False

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
h : Pow2 3
⊢ False
Tactic:
have : (2 : M) ∣ 3 := h.two_dvd (by simp [←two_add_one_eq_three])
State after:
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
h : Pow2 3
this : 2 ∣ 3
⊢ False

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
h : Pow2 3
this : 2 ∣ 3
⊢ False
Tactic:
simp [←two_add_one_eq_three, ←mod_eq_zero_iff_dvd, one_lt_two] at this
State after:
no goals

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
h : Pow2 3
⊢ 1 < 3
Tactic:
simp [←two_add_one_eq_three]
State after:
no goals