simp [hp.df.iff, hpf₁.df.iff, hpf₂.df.iff, hpf₃.df.iff, hpf₄.df.iff, ←imp_iff_not_or]
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 k : ℕ
P : M → M → M → M → Prop
f₁ f₂ f₃ f₄ : (Fin k → M) → M
Γ : SigmaPiDelta
pf₁ : HSemiformula L M (k + 1) (𝚺, m + 1)
hpf₁ : DefinedWithParam (fun v => v 0 = f₁ fun x => v x.succ) pf₁
pf₂ : HSemiformula L M (k + 1) (𝚺, m + 1)
hpf₂ : DefinedWithParam (fun v => v 0 = f₂ fun x => v x.succ) pf₂
pf₃ : HSemiformula L M (k + 1) (𝚺, m + 1)
hpf₃ : DefinedWithParam (fun v => v 0 = f₃ fun x => v x.succ) pf₃
pf₄ : HSemiformula L M (k + 1) (𝚺, m + 1)
hpf₄ : DefinedWithParam (fun v => v 0 = f₄ fun x => v x.succ) pf₄
p : HSemiformula L M 4 (𝚷, m + 1)
hp : DefinedWithParam (fun v => P (v 0) (v 1) (v 2) (v 3)) p
v : Fin k → M
⊢ (fun v => P (f₁ v) (f₂ v) (f₃ v) (f₄ v)) v ↔
    (Semiformula.Evalm M v id)
      ((HSemiformula.rew (Rew.substs (#0 :> fun x => #x.succ.succ.succ.succ)) pf₁).negSigma ⋎
                  (HSemiformula.rew (Rew.substs (#1 :> fun x => #x.succ.succ.succ.succ)) pf₂).negSigma ⋎
                    (HSemiformula.rew (Rew.substs (#2 :> fun x => #x.succ.succ.succ.succ)) pf₃).negSigma ⋎
                      (HSemiformula.rew (Rew.substs (#3 :> fun x => #x.succ.succ.succ.succ)) pf₄).negSigma ⋎
                        HSemiformula.rew [→ #0, #1, #2, #3] p).all.all.all.all.val
no goals