rintro ⟨fs,⟨⟨a, b, ab_in, def_fs⟩, w_fs⟩⟩
case mpr
W : Type
X : List (List Formula × List Program)
M : KripkeModel W
w : W
φ : Formula
g : List Formula × List Program → Formula → List Formula
⊢ (∃ fs, (∃ a b, (a, b) ∈ X ∧ g (a, b) φ = fs) ∧ ∀ f ∈ fs, evaluate M w f) →
    ∃ f, (∃ a b, (a, b) ∈ X ∧ Con (g (a, b) φ) = f) ∧ evaluate M w f
case mpr.intro.intro.intro.intro.intro
W : Type
X : List (List Formula × List Program)
M : KripkeModel W
w : W
φ : Formula
g : List Formula × List Program → Formula → List Formula
fs : List Formula
w_fs : ∀ f ∈ fs, evaluate M w f
a : List Formula
b : List Program
ab_in : (a, b) ∈ X
def_fs : g (a, b) φ = fs
⊢ ∃ f, (∃ a b, (a, b) ∈ X ∧ Con (g (a, b) φ) = f) ∧ evaluate M w f