exact ih _
L : Language
Δ✝¹ Δ₁ Δ₂ Γ : Sequent L
p q r : SyntacticFormula L
C : Set (SyntacticFormula L)
hC : ∀ (f : ℕ → SyntacticTerm L), ∀ p ∈ C, (Rew.rewrite f).hom p ∈ C
Δ : Sequent L
Δ✝ : List (SyntacticFormula L)
p✝ : Semiformula L ℕ (Nat.succ 0)
t✝ : Semiterm L ℕ 0
a✝ : Derivation ([→ t✝].hom p✝ :: Δ✝)
ih : ∀ (f : ℕ → SyntacticTerm L), CutRestricted C a✝ → CutRestricted C (Derivation.rewrite a✝ f)
f : ℕ → SyntacticTerm L
⊢ CutRestricted C a✝ → CutRestricted C (Derivation.rewrite a✝ f)

L : Language
Δ✝¹ Δ₁ Δ₂ Γ : Sequent L
p q r : SyntacticFormula L
C : Set (SyntacticFormula L)
hC : ∀ (f : ℕ → SyntacticTerm L), ∀ p ∈ C, (Rew.rewrite f).hom p ∈ C
Δ : Sequent L
Δ✝ : List (SyntacticFormula L)
p✝ : Semiformula L ℕ (Nat.succ 0)
t✝ : Semiterm L ℕ 0
a✝ : Derivation ([→ t✝].hom p✝ :: Δ✝)
ih : ∀ (f : ℕ → SyntacticTerm L), CutRestricted C a✝ → CutRestricted C (Derivation.rewrite a✝ f)
f : ℕ → SyntacticTerm L
⊢ (∃' (Rew.rewrite (⇑Rew.bShift ∘ f)).hom p✝) :: List.map (⇑(Rew.rewrite f).hom) Δ✝ =
    List.map (⇑(Rew.rewrite f).hom) ((∃' p✝) :: Δ✝)
L : Language
Δ✝¹ Δ₁ Δ₂ Γ : Sequent L
p q r : SyntacticFormula L
C : Set (SyntacticFormula L)
hC : ∀ (f : ℕ → SyntacticTerm L), ∀ p ∈ C, (Rew.rewrite f).hom p ∈ C
Δ : Sequent L
Δ✝ : List (SyntacticFormula L)
p✝ : Semiformula L ℕ (Nat.succ 0)
t✝ : Semiterm L ℕ 0
a✝ : Derivation ([→ t✝].hom p✝ :: Δ✝)
ih : ∀ (f : ℕ → SyntacticTerm L), CutRestricted C a✝ → CutRestricted C (Derivation.rewrite a✝ f)
f : ℕ → SyntacticTerm L
⊢ (∃' (Rew.rewrite (⇑Rew.bShift ∘ f)).hom p✝) :: List.map (⇑(Rew.rewrite f).hom) Δ✝ =
    List.map (⇑(Rew.rewrite f).hom) ((∃' p✝) :: Δ✝)