case gen_ v phi _ ih_2 =>
  intro D I V E _
  simp only [Holds]
  intro d
  apply ih_2
  simp
Δ : List Formula
F : Formula
v : VarName
phi : Formula
a✝ : 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),
    (∀ H ∈ [], Holds D I V E H) → Holds D I V E (forall_ v phi)
no goals