Theorems · Theorem · number theory
Even.neg_zpow
∀ {α : Type u_2} [inst : DivisionMonoid α] [inst_1 : HasDistribNeg α] {n : ℤ}, Even n → ∀ (a : α), (-a) ^ n = a ^ n- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
- Assumes
- DivisionMonoidHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Evenstatement and proof · cited by 444
- DivisionMonoidstatement and proof · cited by 201
- HasDistribNegstatement and proof · cited by 114
- neg_mul_negproof · cited by 32
- zpow_mulproof · cited by 27
- zpow_twoproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Even.neg_one_zpowproof · cited by 1
- Even.zpow_absproof · cited by 0