have hzz := hx z
case a.intro
m : ℕ
f : ℕ → ℕ
hf : ∀ (n : ℕ), f (f n) = n + (2 * m + 1)
f_injective : Function.Injective f
NN : Set ℕ := Set.univ
A : Set ℕ := NN \ f '' NN
B : Set ℕ := f '' A
hid : B = f '' NN \ f '' (f '' NN)
ab_disjoint : Disjoint A B
ab_union : A ∪ B = NN \ f '' (f '' NN)
x : ℕ
H : 2 * m + 1 ≤ x
z : ℕ
hx : ∀ (x : ℕ), ¬f (f x) = 2 * m + 1 + z
hz : x = 2 * m + 1 + z
⊢ False
case a.intro
m : ℕ
f : ℕ → ℕ
hf : ∀ (n : ℕ), f (f n) = n + (2 * m + 1)
f_injective : Function.Injective f
NN : Set ℕ := Set.univ
A : Set ℕ := NN \ f '' NN
B : Set ℕ := f '' A
hid : B = f '' NN \ f '' (f '' NN)
ab_disjoint : Disjoint A B
ab_union : A ∪ B = NN \ f '' (f '' NN)
x : ℕ
H : 2 * m + 1 ≤ x
z : ℕ
hx : ∀ (x : ℕ), ¬f (f x) = 2 * m + 1 + z
hz : x = 2 * m + 1 + z
hzz : ¬f (f z) = 2 * m + 1 + z
⊢ False