Theorems · Theorem · group theory
div_mul_div_cancel
∀ {G : Type u_3} [inst : Group G] (a b c : G), a / b * (b / c) = a / c- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 13 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.
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
- mul_div_assocproof · cited by 149
- div_mul_cancelproof · cited by 33
Cited by13
Results whose statement or proof uses this declaration.
- List.prod_range_div'proof · cited by 2
- div_mul_div_cancel'proof · cited by 2
- div_div_div_cancel_rightproof · cited by 2
- norm_div_le_norm_div_add_norm_divproof · cited by 1
- IsUltrametricDist.norm_div_eq_max_of_norm_div_ne_norm_divproof · cited by 1
- Finset.prod_intervalGapsWithin_mul_prod_eq_divproof · cited by 1
- norm_div_sub_norm_div_le_norm_divproof · cited by 0
- Finset.prod_range_div'proof · cited by 0
- le_map_div_add_map_divproof · cited by 0
- le_map_div_mul_map_divproof · cited by 0
- div_div_div_cancel_leftproof · cited by 0
- NonarchimedeanGroup.cauchySeq_of_tendsto_div_nhds_oneproof · cited by 0