intro v
L : Language
inst✝⁹ : L.ORing
ξ : Type v
n : ℕ
M : Type u_1
inst✝⁸ : Zero M
inst✝⁷ : One M
inst✝⁶ : Add M
inst✝⁵ : Mul M
inst✝⁴ : LT M
inst✝³ : M ⊧ₘ* 𝐏𝐀⁻
inst✝² : Structure L M
inst✝¹ : Structure.ORing L M
inst✝ : Structure.Monotone L M
Γ✝ : HierarchySymbol
k : ℕ
P✝ Q : (Fin k → M) → Prop
m : ℕ
Γ : SigmaPiDelta
P : (Fin k → M) → M → Prop
f : (Fin k → M) → M
bf : HSemiformula L M (k + 1) (𝚺, m + 1)
hbf : DefinedWithParam (fun v => v 0 = f fun x => v x.succ) bf
p : HSemiformula L M k.succ (𝚺, m + 1)
hp : DefinedWithParam (fun w => P (fun x => w x.succ) (w 0)) p
⊢ DefinedWithParam (fun v => ∃ x < f v, P v x)
    (HSemiformula.mkSigma (“∃' (!bf.val ∧ (∃[#0 < #1] !((Rew.substs (#0 :> fun x => #x.succ.succ)).hom p.val)))”) ⋯)
L : Language
inst✝⁹ : L.ORing
ξ : Type v
n : ℕ
M : Type u_1
inst✝⁸ : Zero M
inst✝⁷ : One M
inst✝⁶ : Add M
inst✝⁵ : Mul M
inst✝⁴ : LT M
inst✝³ : M ⊧ₘ* 𝐏𝐀⁻
inst✝² : Structure L M
inst✝¹ : Structure.ORing L M
inst✝ : Structure.Monotone L M
Γ✝ : HierarchySymbol
k : ℕ
P✝ Q : (Fin k → M) → Prop
m : ℕ
Γ : SigmaPiDelta
P : (Fin k → M) → M → Prop
f : (Fin k → M) → M
bf : HSemiformula L M (k + 1) (𝚺, m + 1)
hbf : DefinedWithParam (fun v => v 0 = f fun x => v x.succ) bf
p : HSemiformula L M k.succ (𝚺, m + 1)
hp : DefinedWithParam (fun w => P (fun x => w x.succ) (w 0)) p
v : Fin k → M
⊢ (fun v => ∃ x < f v, P v x) v ↔
    (Semiformula.Evalm M v id)
      (HSemiformula.mkSigma (“∃' (!bf.val ∧ (∃[#0 < #1] !((Rew.substs (#0 :> fun x => #x.succ.succ)).hom p.val)))”)
          ⋯).val