Theorems · Theorem · group theory
inv_mul_cancel_left
∀ {G : Type u_1} [inst : Group G] (a b : G), a⁻¹ * (a * b) = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 88 results in Mathlib
- Foundations
- Depth 7 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
- inv_mul_cancelproof · cited by 107
Cited by88
Results whose statement or proof uses this declaration.
- Set.image_mul_leftproof · cited by 21
- mul_inv_cancel_commproof · cited by 13
- eq_inv_mul_iff_mul_eqproof · cited by 11
- mul_mem_cancel_leftproof · cited by 10
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- mul_div_cancel_leftproof · cited by 9
- mem_leftCoset_iffproof · cited by 6
- inv_mul_eq_iff_eq_mulproof · cited by 5
- Filter.tendsto_atTop_mul_left_of_le'proof · cited by 4
- rightCoset_eq_iffproof · cited by 3
- eq_inv_mul_of_mul_eqproof · cited by 3
- Finset.card_smul_inter_smulproof · cited by 3