aesop
A : Type
R : A → A → Prop
inhabited_A : Nonempty A
P : A → Prop
IH : ∀ (x : A), (∀ (y : A), R x y → P y) → P x
x : A
norm : normalizes R x
h : ¬P x
h' : ∃ f, f 0 = x ∧ ∀ (n : ℕ), ¬P (f n) ∧ R (f n) (f (n + 1))
xs : ℕ → A
P0 : xs 0 = x
P1 : ∀ (n : ℕ), ¬P (xs n) ∧ R (xs n) (xs (n + 1))
⊢ xs 0 = x ∧ ∀ (n : ℕ), R (xs n) (xs (n + 1))
no goals