Theorems · Theorem · group theory
zpow_neg_one
∀ {G : Type u_1} [inst : DivInvMonoid G] (x : G), x ^ (-1) = x⁻¹- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- DivInvMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- pow_oneproof · cited by 894
- DivInvMonoidstatement and proof · cited by 103
- zpow_negSuccproof · cited by 92
Cited by11
Results whose statement or proof uses this declaration.
- padicNorm.int_eq_one_iffproof · cited by 3
- Module.reflection_mul_reflection_zpow_apply_selfproof · cited by 2
- AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zeroproof · cited by 1
- Subgroup.transferTransversal_apply''proof · cited by 1
- Pell.existsUnique_pos_generatorproof · cited by 1
- RatFunc.inftyValuation.X_invproof · cited by 1
- VitaliFamily.withDensity_le_mulproof · cited by 1
- zpow_induction_leftproof · cited by 0
- FractionalIdeal.count_invproof · cited by 0
- DirichletCharacter.conductor_invproof · cited by 0
- circleIntegrable_sub_zpow_iffproof · cited by 0