apply sf
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
P : A → Prop
Q : A → A → Prop
a : A
pa : P a
ex : ∀ (a : A), P a → ∃ b, P b ∧ Q a b
h : ∃ f, f 0 = { val := a, property := pa } ∧ ∀ (n : ℕ), P (f n).val ∧ Q (f n).val (f (n + 1)).val
f : ℕ → { x // P x }
zf : f 0 = { val := a, property := pa }
sf : ∀ (n : ℕ), P (f n).val ∧ Q (f n).val (f (n + 1)).val
n : ℕ
⊢ P (f n).val ∧ Q (f n).val (f (n + 1)).val
no goals