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