apply Set.eq_empty_iff_forall_not_mem.mpr
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
⊢ ↑t ∩ 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
⊢ ∀ (x_1 : Form), ¬x_1 ∈ ↑t ∩ generatedDisjunctions x