Theorems · Theorem · number theory
neg_one_pow_eq_ite
∀ {R : Type u_4} [inst : Monoid R] [inst_1 : HasDistribNeg R] {n : ℕ}, (-1) ^ n = if Even n then 1 else -1- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidHasDistribNeg
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.
- Monoidstatement and proof · cited by 3,887
- Evenstatement and proof · cited by 444
- Oddproof · cited by 364
- HasDistribNegstatement and proof · cited by 114
- Nat.even_or_oddproof · cited by 28
- Even.neg_one_powproof · cited by 20
- Odd.neg_one_powproof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- neg_one_pow_eq_one_iff_evenproof · cited by 5
- neg_one_zpow_eq_iteproof · cited by 1
- neg_one_pow_congrproof · cited by 1
- neg_one_pow_eq_neg_one_iff_oddproof · cited by 1
- Real.coe_intFib_eqproof · cited by 0