Theorem: LO.FirstOrder.Arith.Model.isPrime_defined (Arithmetization/Basic/PeanoMinus.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* 𝐏𝐀⁻
a b c : M
⊢ 𝚺₀-Predicate fun a => IsPrime a via isPrimedef
Tactic:
intro v
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* 𝐏𝐀⁻
a b c : M
v : Fin 1 → M
⊢ (fun v => (fun a => IsPrime a) (v 0)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val isPrimedef)

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* 𝐏𝐀⁻
a b c : M
v : Fin 1 → M
⊢ (fun v => (fun a => IsPrime a) (v 0)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val isPrimedef)
Tactic:
simp [Semiformula.eval_substs, Matrix.comp_vecCons', Matrix.vecHead, Matrix.constant_eq_singleton,
  IsPrime, isPrimedef]
State after:
no goals