Theorem: LO.FirstOrder.Arith.Model.sqrt_defined (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
⊢ 𝚺₀-Function₁ fun a => √a via sqrtDef
Tactic:
intro v
State after:
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
v : Fin (Nat.succ 1) → M
⊢ (fun v => v 0 = (fun v => (fun a => √a) (v 0)) fun x => v x.succ) v ↔
    (Semiformula.Evalbm M v) (HSemiformula.val sqrtDef)

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
v : Fin (Nat.succ 1) → M
⊢ (fun v => v 0 = (fun v => (fun a => √a) (v 0)) fun x => v x.succ) v ↔
    (Semiformula.Evalbm M v) (HSemiformula.val sqrtDef)
Tactic:
simp[sqrt_graph, sqrtDef, Matrix.vecHead, Matrix.vecTail]
State after:
no goals