powersetCard_one — Mathlib

English

Same decomposition as powerset_insert: powerset (insert a s) = s.powerset ∪ s.powerset.image (insert a).

Русский

Та же декомпозиция: powerset (insert a s) = s.powerset ∪ s.powerset.image(insert a).

LaTeX

$$$\text{powerset}(\text{insert}(a,s)) = \text{powerset}(s) \cup \text{powerset}(s).image(\text{insert}(a))$$$

Lean4

theorem powersetCard_one (s : Finset α) : s.powersetCard 1 = s.map ⟨_, Finset.singleton_injective⟩ :=
  eq_of_veq <| Multiset.map_injective val_injective <| by simp [Multiset.powersetCard_one]

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