simp
case a.a
φ : Formula
R L : Finset Formula
valid_proj : ~(□φ) ∈ R
ℓ : Char
ℓ_in_proj : ℓ ∈ voc (diamondProjectTNode (Sum.inr φ) (L, R)).1 ∩ voc (diamondProjectTNode (Sum.inr φ) (L, R)).2
ℓ_left : ∃ a ∈ projection L, ℓ ∈ vocabOfFormula a
⊢ ℓ ∈ voc (projection (L, R).1)
case a.a
φ : Formula
R L : Finset Formula
valid_proj : ~(□φ) ∈ R
ℓ : Char
ℓ_in_proj : ℓ ∈ voc (diamondProjectTNode (Sum.inr φ) (L, R)).1 ∩ voc (diamondProjectTNode (Sum.inr φ) (L, R)).2
ℓ_left : ∃ a ∈ projection L, ℓ ∈ vocabOfFormula a
⊢ ∃ a ∈ projection L, ℓ ∈ vocabOfFormula a