intros f g h₃
t : Th
x : Form
h₁ : x ∈ ⋂₀ { p | isPrimeTheory p ∧ ↑t ≤ p ∧ formalTheory p }
h₂ : ¬x ∈ ↑t
l₁ : ∀ (g : Form), g ∈ generatedDisjunctions x → {g}⊢x
l₂ : ↑t ∩ generatedDisjunctions x = ∅
⊢ isDisjunctionClosed (generatedDisjunctions x)
t : Th
x : Form
h₁ : x ∈ ⋂₀ { p | isPrimeTheory p ∧ ↑t ≤ p ∧ formalTheory p }
h₂ : ¬x ∈ ↑t
l₁ : ∀ (g : Form), g ∈ generatedDisjunctions x → {g}⊢x
l₂ : ↑t ∩ generatedDisjunctions x = ∅
f g : Form
h₃ : f ∈ generatedDisjunctions x ∧ g ∈ generatedDisjunctions x
⊢ f¦g ∈ generatedDisjunctions x