Theorems · Theorem · number theory
Fin.even_iff
∀ {n : ℕ} {k : Fin n}, Even k ↔ Odd n ∨ Even ↑kIn Fin n, all elements are even for odd n,
otherwise an element is even iff its Fin.val value is even.
- Defined in
- Mathlib.Data.Fin.Parity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Evenstatement and proof · cited by 444
- Oddstatement and proof · cited by 364
- Nat.not_even_iff_oddproof · cited by 34
- imp_iff_not_orproof · cited by 12
- Fin.even_iff_of_evenproof · cited by 4
- Fin.even_of_valproof · cited by 3
- Fin.even_of_oddproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Fin.even_iff_impproof · cited by 0