inclusion_exclusion_card_inf_compl

English

There is a decidable equality instance for partitions of a fixed n: for any n, Nat.Partition n has a decidable equality.

Русский

Существует разрешимая по равенству инстанция для разбиений с фиксированным n: для данного n множество Partitions n имеет decidableEq.

LaTeX

$$$ \text{DecidableEq} (n\text{-Partition}) $$$

Lean4

/-- **Inclusion-exclusion principle** for the cardinality of an intersection of complements.

The cardinality of the intersection of the complements of the `S i` over `i ∈ s` is the
alternating sum of the cardinalities of the intersections of the `S i`. -/
theorem inclusion_exclusion_card_inf_compl (s : Finset ι) (S : ι → Finset α) :
    #(s.inf fun i ↦ (S i)ᶜ) = ∑ t ∈ s.powerset, (-1 : ℤ) ^ #t * #(t.inf S) := by
  simpa using inclusion_exclusion_sum_inf_compl (G := ℤ) s S (f := 1)

Похожие утверждения