Theorem: LO.FirstOrder.Arith.Model.pair_mem_product_iff (Arithmetization/ISigmaOne/HFS/Basic.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* 𝐈𝚺₁
x y a b : M
⊢ ⟪x, y⟫ ∈ a ×ʰᶠ b ↔ x ∈ a ∧ y ∈ b
Tactic:
simp [mem_product_iff']
State after:
no goals