Theorems · Definition · number theory
Odd
{α : Type u_2} → [Semiring α] → α → PropAn element a of a semiring is odd if there exists k such a = 2*k + 1.
- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 364 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 166 definitions · uses propext
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
Cited by378
Results whose statement or proof uses this declaration.
- Nat.not_even_iff_oddstatement · cited by 34
- Nat.even_or_oddstatement · cited by 28
- Odd.neg_one_powstatement and proof · cited by 18
- Odd.neg_powstatement and proof · cited by 14
- Nat.odd_iffstatement and proof · cited by 14
- HomologicalComplex.alternatingConststatement and proof · cited by 13
- odd_onestatement · cited by 12
- Nat.not_odd_iff_evenstatement · cited by 12
- bernoulli_eq_bernoulli'_of_ne_oneproof · cited by 10
- SimpleGraph.oddComponentsproof · cited by 10
- Odd.posstatement and proof · cited by 9
- Int.not_even_iff_oddstatement · cited by 8
Showing the 200 most cited of 378.