Theorems · Theorem · group theory
inv_pow
∀ {α : Type u_1} [inst : DivisionMonoid α] (a : α) (n : ℕ), a⁻¹ ^ n = (a ^ n)⁻¹- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 140 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 86 definitions · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivisionMonoidstatement and proof · cited by 201
Cited by140
Results whose statement or proof uses this declaration.
- div_powproof · cited by 66
- zpow_mulproof · cited by 27
- tendsto_pow_atTop_nhds_zero_of_lt_oneproof · cited by 18
- exists_pow_lt_of_lt_oneproof · cited by 16
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- inv_zpowproof · cited by 10
- ENNReal.inv_powproof · cited by 9
- PiNat.dist_eq_of_neproof · cited by 7
- Rat.cast_powproof · cited by 7
- PiNat.mem_cylinder_iff_dist_leproof · cited by 4
- hasSum_geometric_two'proof · cited by 4
- IsDiscreteValuationRing.intValuation_maximalIdealproof · cited by 3