constructor
x : ℕ
⊢ x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} ↔ x ∈ Set.singleton 0
case mp
x : ℕ
⊢ x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m} → x ∈ Set.singleton 0

case mpr
x : ℕ
⊢ x ∈ Set.singleton 0 → x ∈ ⋂ j, {m | m ≤ 2 * j ∧ Even m}