Theorem: LO.FirstOrder.Arith.Model.LenBit.iff_rem (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* 𝐈open
i a : M
⊢ LenBit i a ↔ a / i % 2 = 1
Tactic:
simp [LenBit]
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* 𝐈open
i a : M
⊢ ¬2 ∣ a / i ↔ a / i % 2 = 1

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* 𝐈open
i a : M
⊢ ¬2 ∣ a / i ↔ a / i % 2 = 1
Tactic:
rcases mod_two (a / i) with (h | h) <;> simp [h, ←mod_eq_zero_iff_dvd]
State after:
no goals