Theorems · Theorem · number theory
neg_one_zpow_eq_ite
∀ {α : Type u_2} [inst : DivisionMonoid α] [inst_1 : HasDistribNeg α] {n : ℤ}, (-1) ^ n = if Even n then 1 else -1- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionMonoidHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Evenstatement and proof · cited by 444
- inv_oneproof · cited by 301
- zpow_natCastproof · cited by 271
- DivisionMonoidstatement and proof · cited by 201
- zpow_negproof · cited by 198
- HasDistribNegstatement and proof · cited by 114
- inv_negproof · cited by 42
- neg_one_pow_eq_iteproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Int.coe_fib_negproof · cited by 0