simp only [Holds]
Δ : List Formula
F : Formula
v : VarName
phi : Formula
a✝¹ : IsDeduct [] phi
ih_2 :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), (∀ H ∈ [], Holds D I V E H) → Holds D I V E phi
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
a✝ : ∀ H ∈ [], Holds D I V E H
⊢ Holds D I V E (forall_ v phi)
Δ : List Formula
F : Formula
v : VarName
phi : Formula
a✝¹ : IsDeduct [] phi
ih_2 :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), (∀ H ∈ [], Holds D I V E H) → Holds D I V E phi
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
a✝ : ∀ H ∈ [], Holds D I V E H
⊢ ∀ (d : D), Holds D I (Function.updateITE V v d) E phi