clear prf₁ prf₂ prf₃ prf₄
case a
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (▲{f}) ↑u ⊆ ↑↑p }
l₂ : ↑t ∩ Δ = ∅
P Q R S : Form
l₆ : S ∈ ↑u
prf₁ : BProof {P} (S⊃R)
T U : Form
l₁₀ : U ∈ ↑u
prf₂ : BProof {Q} (U⊃T)
prf₃ : BProof {P} (S&U⊃R¦T)
prf₄ : BProof {Q} (S&U⊃R¦T)
prf₅ : BProof {P¦Q} (S&U⊃R¦T)
⊢ R¦T ∈ formalApplication (▲{P¦Q}) ↑u
case a
t u : Th
p : Pr
h₁ : formalApplicationFunction t u ≤ ↑p
Δ : Set Form := { f | ¬formalApplication (▲{f}) ↑u ⊆ ↑↑p }
l₂ : ↑t ∩ Δ = ∅
P Q R S : Form
l₆ : S ∈ ↑u
T U : Form
l₁₀ : U ∈ ↑u
prf₅ : BProof {P¦Q} (S&U⊃R¦T)
⊢ R¦T ∈ formalApplication (▲{P¦Q}) ↑u