obtain ⟨p, hp⟩ := noLEM (α := α)
case right
α : Type
inst✝ : Inhabited α
⊢ ∃ f, 𝐂𝐥 ⊢! f ∧ ¬𝐈𝐧𝐭 ⊢! f
case right.intro
α : Type
inst✝ : Inhabited α
p : Formula α
hp : 𝐈𝐧𝐭 ⊬! p ⋎ ~p
⊢ ∃ f, 𝐂𝐥 ⊢! f ∧ ¬𝐈𝐧𝐭 ⊢! f