Theorems · Theorem · group theory
inv_inj
∀ {G : Type u_3} [inst : InvolutiveInv G] {a b : G}, a⁻¹ = b⁻¹ ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- InvolutiveInv
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- InvolutiveInvstatement and proof · cited by 102
- inv_injectiveproof · cited by 17
Cited by25
Results whose statement or proof uses this declaration.
- zpow_mulproof · cited by 27
- inv_mul_eq_oneproof · cited by 11
- PowerSeries.IsWeierstrassFactorization.elimproof · cited by 5
- LaurentSeries.valuation_single_zpowproof · cited by 3
- IsPrimitiveRoot.invproof · cited by 2
- Set.inv_mem_centerproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation_liesOverproof · cited by 1
- NormedDivisionRing.norm_eq_one_iff_ne_zero_of_discreteproof · cited by 1
- IsPrimitiveRoot.zpow_eq_one_iff_dvdproof · cited by 1
- ENNReal.HolderTriple.uniqueproof · cited by 1
- ENNReal.HolderTriple.unique_of_ne_zeroproof · cited by 1
- Subgroup.closure_mul_image_mul_eq_topproof · cited by 1