intros A Q inhab forall_exists_Q
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
⊢ ∀ {A : Sort u_1} (Q : A → A → Prop), Inhabited A → (∀ (a : A), ∃ b, Q a b) → ∃ f, ∀ (n : ℕ), Q (f n) (f (n + 1))
A✝ : Type
R : A✝ → A✝ → Prop
inhabited_A : Nonempty A✝
A : Sort u_1
Q : A → A → Prop
inhab : Inhabited A
forall_exists_Q : ∀ (a : A), ∃ b, Q a b
⊢ ∃ f, ∀ (n : ℕ), Q (f n) (f (n + 1))