clear l₈ l₁₂ l₁₃ h₂
case a
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (↑t) (▲{f}) ⊆ ↑↑p }
l₂ : ↑u ∩ Δ = ∅
P Q : Form
h₂ : formalApplication (↑t) (▲{P¦Q}) ⊆ ↑↑p
R S : Form
prf₁ : BProof {P} S
l₆ : S⊃R ∈ ↑t
l₈ : ¬R ∈ ↑↑p
T U : Form
prf₂ : BProof {Q} U
l₁₀ : U⊃T ∈ ↑t
l₁₂ : ¬T ∈ ↑↑p
l₁₃ : ¬R¦T ∈ p
⊢ R¦T ∈ formalApplication (↑t) (▲{P¦Q})
case a
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (↑t) (▲{f}) ⊆ ↑↑p }
l₂ : ↑u ∩ Δ = ∅
P Q R S : Form
prf₁ : BProof {P} S
l₆ : S⊃R ∈ ↑t
T U : Form
prf₂ : BProof {Q} U
l₁₀ : U⊃T ∈ ↑t
⊢ R¦T ∈ formalApplication (↑t) (▲{P¦Q})