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' : Formula
a2 : H' ∈ Δ'
a1_left : Holds D I V E H
a1_right : ∀ a ∈ Δ', Holds D I V E a
⊢ Holds D I V E H'
no goals