Theorems · Theorem · group theory
self_eq_inv
∀ {G : Type u_2} [inst : Group G] [IsMulTorsionFree G] {a : G}, a = a⁻¹ ↔ a = 1- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupIsMulTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- sqproof · cited by 280
- IsMulTorsionFreestatement and proof · cited by 44
- mul_eq_one_iff_eq_invproof · cited by 12
- sq_eq_oneproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- inv_eq_selfproof · cited by 1
- self_ne_invproof · cited by 0