case struct_1_ Δ' H _ _ ih_2 =>
  intro D I V E a1
  apply ih_2
  intro H' a2
  simp at a1
  cases a1
  case _ a1_left a1_right =>
    exact a1_right H' a2
Δ : List Formula
F : Formula
Δ' : List Formula
H phi✝ : Formula
a✝ : IsDeduct Δ' phi✝
ih_2 :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), (∀ H ∈ Δ', Holds D I V E H) → Holds D I V E phi✝
⊢ ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H_1 ∈ H :: Δ', Holds D I V E H_1) → Holds D I V E phi✝
no goals