Theorems · Theorem · number theory
Even.neg_pow
∀ {α : Type u_2} [inst : Monoid α] [inst_1 : HasDistribNeg α] {n : ℕ}, Even n → ∀ (a : α), (-a) ^ n = a ^ n- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 23 from the axioms, rests on 252 definitions · uses propext
- Assumes
- MonoidHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- pow_mulproof · cited by 210
- HasDistribNegstatement and proof · cited by 114
- neg_sqproof · cited by 31
Cited by99
Results whose statement or proof uses this declaration.
- Even.neg_one_powproof · cited by 20
- groupHomology.comp_d₂₁_eqproof · cited by 10
- Int.cast_negOnePowproof · cited by 10
- Complex.cos_argproof · cited by 7
- Real.arctan_negproof · cited by 6
- orderOf_neg_oneproof · cited by 5
- Int.fib_negproof · cited by 4
- Int.fib_neg_natCastproof · cited by 4
- WeierstrassCurve.ΨSq_negproof · cited by 4
- Matrix.adjugate_fin_twoproof · cited by 3
- Polynomial.resultant_add_right_degproof · cited by 3
- Matrix.isElliptic_neg_iffproof · cited by 3