Theorems · Theorem · number theory
Finset.even_sum_iff_even_card_odd
∀ {ι : Type u_1} {s : Finset ι} (f : ι → ℕ), Even (∑ i ∈ s, f i) ↔ Even {x ∈ s | Odd (f x)}.card- Defined in
- Mathlib.Algebra.BigOperators.Ring.Nat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- Finset.cardstatement and proof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- Finset.filterstatement and proof · cited by 949
- Evenstatement and proof · cited by 444
- Oddstatement and proof · cited by 364
- Finset.sum_filterproof · cited by 37
- Finset.card_eq_sum_onesproof · cited by 22
- Finset.sum_filter_add_sum_filter_notproof · cited by 20
- Nat.odd_iffproof · cited by 14
- Nat.even_iffproof · cited by 8
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