Theorems · Theorem · group theory
mul_inv_cancel
∀ {G : Type u_1} [inst : Group G] (a : G), a * a⁻¹ = 1- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 128 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 34 definitions · uses no axioms
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- inv_mul_cancelproof · cited by 107
Cited by130
Results whose statement or proof uses this declaration.
- mul_inv_cancel_leftproof · cited by 86
- smul_inv_smulproof · cited by 53
- mul_inv_cancel_rightproof · cited by 53
- div_self'proof · cited by 25
- Group.isUnitproof · cited by 18
- isConj_iffproof · cited by 16
- inv_le_inv_iffproof · cited by 11
- inv_lt_inv_iffproof · cited by 9
- injective_iff_map_eq_oneproof · cited by 9
- Representation.self_inv_applyproof · cited by 8
- toUnitsproof · cited by 8
- eq_mul_inv_of_mul_eqproof · cited by 7