intro H' a2
case a
Δ : List Formula
F : Formula
Δ' : List Formula
phi psi : Formula
a✝¹ : IsDeduct Δ' (phi.imp_ psi)
a✝ : IsDeduct Δ' phi
ih_minor :
  ∀ (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
a1 : ∀ H ∈ Δ', Holds D I V E H
ih_major :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H ∈ Δ', Holds D I V E H) → Holds D I V E phi → Holds D I V E psi
⊢ ∀ H ∈ Δ', Holds D I V E H
case a
Δ : List Formula
F : Formula
Δ' : List Formula
phi psi : Formula
a✝¹ : IsDeduct Δ' (phi.imp_ psi)
a✝ : IsDeduct Δ' phi
ih_minor :
  ∀ (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
a1 : ∀ H ∈ Δ', Holds D I V E H
ih_major :
  ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H ∈ Δ', Holds D I V E H) → Holds D I V E phi → Holds D I V E psi
H' : Formula
a2 : H' ∈ Δ'
⊢ Holds D I V E H'