have l₂ : ↑t ∩ Δ = ∅ := by
  apply Set.eq_empty_iff_forall_not_mem.mpr
  intros P h₂
  have l₃ : ▲{P} ⊆ ↑t := generatedContained (Set.singleton_subset_iff.mpr h₂.left)
  have l₄ := formalAppMonotoneRight ↑u l₃
  exact h₂.right $ le_trans l₄ h₁
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (▲{f}) ↑u ⊆ ↑↑p }
⊢ ∃ q, t ≤ ↑q ∧ formalApplication ↑↑q ↑u ⊆ ↑↑p
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (▲{f}) ↑u ⊆ ↑↑p }
l₂ : ↑t ∩ Δ = ∅
⊢ ∃ q, t ≤ ↑q ∧ formalApplication ↑↑q ↑u ⊆ ↑↑p