Set: pp::colors
  Set: pp::unicode
  Assumed: f
  Assumed: g
∀ a b : Type, ∃ c : Type, g a b = f c
∀ a b : Type, ∃ c : Type, g a b = f c : Bool
∀ (a b : Type), (∀ (x : Type), g a b == f x → ⊥) → ⊥