English
For Finset powerset, membership characterizes as subset containment: s ∈ powerset t iff s ⊆ t.
Русский
Для множества подмножеств Finset: s ∈ powerset t эквивалентно s ⊆ t.
LaTeX
$$$$ s \\in \\text{powerset}(t) \\;\\Longleftrightarrow\\; s \\subseteq t. $$$$
Lean4
@[simp, grind =]
theorem mem_powerset {s t : Finset α} : s ∈ powerset t ↔ s ⊆ t :=
by
cases s
simp [powerset, mem_mk, mem_pmap, mk.injEq, exists_prop, exists_eq_right, ← val_le_iff]