Theorem: LO.FirstOrder.Arith.Model.Exponential.seqₛ_one_zero_two (Arithmetization/ISigmaZero/Exponential/Exp.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
⊢ Seqₛ 1 seqX₀ seqY₀
Tactic:
intro u leu
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
u : M
leu : u ≤ 1
⊢ u ≠ 2 → PPow2 u → Seqₛ.Even seqX₀ seqY₀ u ∨ Seqₛ.Odd seqX₀ seqY₀ u

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
u : M
leu : u ≤ 1
⊢ u ≠ 2 → PPow2 u → Seqₛ.Even seqX₀ seqY₀ u ∨ Seqₛ.Odd seqX₀ seqY₀ u
Tactic:
rcases le_one_iff_eq_zero_or_one.mp leu with (rfl | rfl) <;> simp
State after:
no goals