Variable f : Type -> Bool Show forall a b : Type, (f a) = (f b) Variable g : Bool -> Bool -> Bool Show forall (a b : Type) (c : Bool), g c ((f a) = (f b)) Show exists (a b : Type) (c : Bool), g c ((f a) = (f b)) Show forall (a b : Type) (c : Bool), (g c (f a) = (f b)) ⇒ (f a) Check forall (a b : Type) (c : Bool), g c ((f a) = (f b)) Show ∀ (a b : Type) (c : Bool), g c ((f a) = (f b)) Show ∀ a b : Type, (f a) = (f b) Show ∃ a b : Type, (f a) = (f b) ∧ (f a) Show ∃ a b : Type, (f a) = (f b) ∨ (f b) Variable a : Bool Show (f a) ∨ (f a) Show (f a) = a ∨ (f a) Show (f a) = a ∧ (f a)