Theorems · Theorem · group theory
inv_zpow
∀ {α : Type u_1} [inst : DivisionMonoid α] (a : α) (n : ℤ), a⁻¹ ^ n = (a ^ n)⁻¹- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zpow_natCastproof · cited by 271
- DivisionMonoidstatement and proof · cited by 201
- inv_powproof · cited by 140
- zpow_negSuccproof · cited by 92
Cited by10
Results whose statement or proof uses this declaration.
- inv_zpow'proof · cited by 7
- div_zpowproof · cited by 4
- CoxeterSystem.prod_alternatingWord_eq_prod_alternatingWord_subproof · cited by 2
- Module.reflection_mul_reflection_zpow_applyproof · cited by 1
- Padic.norm_p_zpowproof · cited by 1
- Equiv.Perm.isCycle_swap_mul_aux₂proof · cited by 1
- circleIntegral.integral_sub_inv_of_mem_ballproof · cited by 1
- smul_eq_self_of_preimage_zpow_eq_selfproof · cited by 0
- one_div_zpowproof · cited by 0
- MulAction.period_invproof · cited by 0