exact this v
M : Type u_1
inst✝¹⁰ : Zero M
inst✝⁹ : One M
inst✝⁸ : Add M
inst✝⁷ : Mul M
inst✝⁶ : LT M
inst✝⁵ : M ⊧ₘ* 𝐏𝐀⁻
L : Language
inst✝⁴ : L.ORing
inst✝³ : Structure L M
inst✝² : Structure.ORing L M
inst✝¹ : Structure.Monotone L M
C : Semiformula L ℕ 1 → Prop
inst✝ : M ⊧ₘ* Theory.indScheme L C
p : Semiformula L ℕ 1
hp : C p
v : ℕ → M
this :
  ∀ (ε : ℕ → M),
    (Semiformula.Eval inst✝³ ![0] ε) p →
      (∀ (x : M), (Semiformula.Eval inst✝³ ![x] ε) p → (Semiformula.Eval inst✝³ ![x + 1] ε) p) →
        ∀ (x : M), (Semiformula.Eval inst✝³ ![x] ε) p
⊢ (Semiformula.Evalm M ![0] v) p →
    (∀ (x : M), (Semiformula.Evalm M ![x] v) p → (Semiformula.Evalm M ![x + 1] v) p) →
      ∀ (x : M), (Semiformula.Evalm M ![x] v) p
no goals