Theorem: LO.FirstOrder.Arith.Model.exists_unique_exponential_sq_length (Arithmetization/OmegaOne/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* 𝐈𝚫₀ + 𝛀₁
x : M
⊢ ∃! y, Exponential (‖x‖ ^ 2) y
Tactic:
rcases exists_exponential_sq_length x with ⟨y, h⟩
State after:
case intro
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 + 𝛀₁
x y : M
h : Exponential (‖x‖ ^ 2) y
⊢ ∃! y, Exponential (‖x‖ ^ 2) y

State before:
case intro
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 + 𝛀₁
x y : M
h : Exponential (‖x‖ ^ 2) y
⊢ ∃! y, Exponential (‖x‖ ^ 2) y
Tactic:
exact ExistsUnique.intro y h (fun y' h' ↦ h'.uniq h)
State after:
no goals