Theorems · Theorem · group theory
AddCommute.all
∀ {S : Type u_3} [inst : AddCommMagma S] (a b : S), AddCommute a b- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddCommMagma
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.
- add_commproof · cited by 1,535
- AddCommutestatement · cited by 185
- AddCommMagmastatement and proof · cited by 32
Cited by12
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.map_isAddRegularproof · cited by 1
- AddMonoid.exists_addOrderOf_eq_exponentproof · cited by 1
- approxAddOrderOf.vadd_eq_of_mul_dvdproof · cited by 1
- approxAddOrderOf.vadd_subset_of_coprimeproof · cited by 1
- AddSubmonoid.LocalizationMap.injective_iffproof · cited by 1
- IsOfFinAddOrder.addproof · cited by 0
- AddSubmonoid.LocalizationMap.isCancelAddproof · cited by 0
- List.CommMonoid.sum_insertIdxproof · cited by 0
- AddLocalization.mk_nsmulproof · cited by 0
- Multiset.noncommSum_eq_sumstatement and proof · cited by 0
- Finset.noncommSum_eq_sumstatement and proof · cited by 0
- List.CommMonoid.add_sum_eraseIdxproof · cited by 0