apply h
case inr
A B : Set ℕ
n : ℕ
hA : 0 ∈ A
hB : 0 ∈ B
hc : n ≤ countelements A n + countelements B n
h : n ∉ A + B
hnA : n ∉ A
hnB : n ∉ B
hca : countelements A (n - 1) = countelements A n
hcb : countelements B (n - 1) = countelements B n
hn1 : n > 0
⊢ False
case inr
A B : Set ℕ
n : ℕ
hA : 0 ∈ A
hB : 0 ∈ B
hc : n ≤ countelements A n + countelements B n
h : n ∉ A + B
hnA : n ∉ A
hnB : n ∉ B
hca : countelements A (n - 1) = countelements A n
hcb : countelements B (n - 1) = countelements B n
hn1 : n > 0
⊢ n ∈ A + B