change formalApplication (lindenbaumExtension t Δ) ↑u ⊆ p
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (▲{f}) ↑u ⊆ ↑↑p }
l₄ : lindenbaumExtension t Δ ∩ Δ = ∅
⊢ formalApplication
      ↑↑{
            val :=
              { val := lindenbaumExtension t Δ,
                property := (_ : ∀ {f : Form}, f ∈ lindenbaumExtension t Δ ↔ lindenbaumExtension t Δ⊢f) },
            property :=
              (_ :
                ∀ {f g : Form},
                  f¦g ∈ lindenbaumExtension t Δ → f ∈ lindenbaumExtension t Δ ∨ g ∈ lindenbaumExtension t Δ) }
      ↑u ⊆
    ↑↑p
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (▲{f}) ↑u ⊆ ↑↑p }
l₄ : lindenbaumExtension t Δ ∩ Δ = ∅
⊢ formalApplication (lindenbaumExtension t Δ) ↑u ⊆ ↑↑p