Theorem: LO.FirstOrder.Arith.Model.pair_ext_iff (Arithmetization/Basic/IOpen.lean)

State before:
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : M ⊧ₘ* 𝐏𝐀⁻
inst✝ : M ⊧ₘ* 𝐈open
a₁ a₂ b₁ b₂ : M
⊢ a₁ = a₂ ∧ b₁ = b₂ → ⟪a₁, b₁⟫ = ⟪a₂, b₂⟫
Tactic:
rintro ⟨rfl, rfl⟩
State after:
case intro
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : M ⊧ₘ* 𝐏𝐀⁻
inst✝ : M ⊧ₘ* 𝐈open
a₁ b₁ : M
⊢ ⟪a₁, b₁⟫ = ⟪a₁, b₁⟫

State before:
case intro
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : M ⊧ₘ* 𝐏𝐀⁻
inst✝ : M ⊧ₘ* 𝐈open
a₁ b₁ : M
⊢ ⟪a₁, b₁⟫ = ⟪a₁, b₁⟫
Tactic:
simp
State after:
no goals