simp at a2
Δ : List Formula
F : Formula
Δ' : List Formula
H phi✝ : Formula
a✝ : IsDeduct (H :: H :: Δ') phi✝
ih_2 :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H_1 ∈ H :: 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
H' : Formula
a2 : H' ∈ H :: 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'
Δ : List Formula
F : Formula
Δ' : List Formula
H phi✝ : Formula
a✝ : IsDeduct (H :: H :: Δ') phi✝
ih_2 :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H_1 ∈ H :: 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
H' : Formula
a1_left : Holds D I V E H
a1_right : ∀ a ∈ Δ', Holds D I V E a
a2 : H' = H ∨ H' ∈ Δ'
⊢ Holds D I V E H'