Theorems · Theorem · group theory
mul_inv_cancel_left
∀ {G : Type u_1} [inst : Group G] (a b : G), a * (a⁻¹ * b) = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- mul_inv_cancelproof · cited by 128
Cited by86
Results whose statement or proof uses this declaration.
- Set.image_mul_leftproof · cited by 21
- eq_inv_mul_iff_mul_eqproof · cited by 11
- Subgroup.comap_map_eqproof · cited by 9
- inv_mul_lt_iff_lt_mulproof · cited by 6
- mem_leftCoset_iffproof · cited by 6
- inv_mul_eq_iff_eq_mulproof · cited by 5
- inv_mul_le_iff_le_mulproof · cited by 5
- Subgroup.isComplement_singleton_univproof · cited by 3
- Subgroup.isOpen_of_mem_nhdsproof · cited by 3
- Subgroup.leftTransversals.diff_mul_diffproof · cited by 3
- mul_inv_le_inv_mul_iffproof · cited by 3
- Finset.card_smul_inter_smulproof · cited by 3