exact a2
case a.left
Δ : List Formula
F : Formula
Δ' : List Formula
H phi : Formula
a✝ : IsDeduct (H :: Δ') phi
ih_2 :
  ∀ (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
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
a1 : ∀ H ∈ Δ', Holds D I V E H
a2 : Holds D I V E H
⊢ Holds D I V E H
no goals