Theorems · Theorem · group theory
div_mul_cancel
∀ {G : Type u_1} [inst : Group G] (a b : G), a / b * b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- div_eq_mul_invproof · cited by 715
- inv_mul_cancel_rightproof · cited by 70
Cited by33
Results whose statement or proof uses this declaration.
- div_mul_div_cancelproof · cited by 13
- HasProd.updateproof · cited by 3
- mabs_div_mabs_le_mabs_divproof · cited by 2
- MonoidHom.surjective_of_surjective_of_surjective_of_injectiveproof · cited by 2
- norm_le_norm_add_norm_div'proof · cited by 2
- Set.image_div_leftproof · cited by 2
- Subgroup.exists_isLeast_one_ltproof · cited by 2
- div_smul_div_commproof · cited by 1
- Multipliable.trans_divproof · cited by 1
- IsMulIndecomposable.pairwise_div_notMem_rangeproof · cited by 1
- Subgroup.mk_goursatFst_eq_iff_mk_goursatSnd_eqproof · cited by 1
- tendsto_div_nhds_one_iff_eqproof · cited by 1