simp_all
W : Type
X : List (List Formula × List Program)
M : KripkeModel W
w : W
φ : Formula
g : List Formula × List Program → Formula → List Formula
⊢ (∃ f ∈ List.map (fun Fδ => Con (g Fδ φ)) X, evaluate M w f) ↔
    ∃ fs ∈ List.map (fun Fδ => g Fδ φ) X, ∀ f ∈ fs, evaluate M w f
W : Type
X : List (List Formula × List Program)
M : KripkeModel W
w : W
φ : Formula
g : List Formula × List Program → Formula → List Formula
⊢ (∃ f, (∃ a b, (a, b) ∈ X ∧ Con (g (a, b) φ) = f) ∧ evaluate M w f) ↔
    ∃ fs, (∃ a b, (a, b) ∈ X ∧ g (a, b) φ = fs) ∧ ∀ f ∈ fs, evaluate M w f