Theorems · Definition · group theory
AddCommute
{S : Type u_3} → [Add S] → S → S → PropTwo elements additively commute if a + b = b + a
- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 185 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSemiconjByproof · cited by 56
Cited by200
Results whose statement or proof uses this declaration.
- Finset.noncommSumstatement and proof · cited by 24
- AddCommute.eqstatement and proof · cited by 18
- AddCommute.symmstatement and proof · cited by 18
- Multiset.noncommSumstatement and proof · cited by 18
- AddCommute.allstatement · cited by 12
- AddCommute.reflstatement · cited by 12
- Multiset.noncommSum_coestatement and proof · cited by 11
- Finset.noncommSum_lemmastatement and proof · cited by 10
- IsAddCentral.commstatement · cited by 10
- AddCommute.mapstatement and proof · cited by 9
- addCommute_iff_eqstatement · cited by 9
- AddMonoidHom.noncommPiCoprodstatement and proof · cited by 8