Theorems · Theorem · group theory
zpow_neg
∀ {α : Type u_1} [inst : DivisionMonoid α] (a : α) (n : ℤ), a ^ (-n) = (a ^ n)⁻¹- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 198 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 104 definitions · uses propext
- Assumes
- DivisionMonoid
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.
- pow_zeroproof · cited by 1,094
- inv_invproof · cited by 494
- inv_oneproof · cited by 301
- zpow_natCastproof · cited by 271
- DivisionMonoidstatement and proof · cited by 201
- zpow_ofNatproof · cited by 144
- zpow_negSuccproof · cited by 92
- DivInvMonoid.zpow_neg'proof · cited by 4
Cited by198
Results whose statement or proof uses this declaration.
- zpow_mulproof · cited by 27
- zpow_posproof · cited by 22
- zpow_add_oneproof · cited by 18
- zpow_subproof · cited by 15
- zpow_sub₀proof · cited by 14
- Int.negOnePow_negproof · cited by 13
- zpow_add_one₀proof · cited by 9
- AnalyticAt.zpowproof · cited by 8
- PadicInt.norm_le_pow_iff_mem_span_powproof · cited by 7
- zpow_nonnegproof · cited by 7
- padicNorm.eq_zpow_of_nonzeroproof · cited by 7
- inv_zpow'proof · cited by 7