Theorems · Definition · group theory
IsAddUnit
{M : Type u_1} → [AddMonoid M] → M → PropAn element a : M of an AddMonoid is an AddUnit if it has a two-sided
additive inverse. The actual definition says that a is equal to some u : AddUnits M,
where AddUnits M is a bundled version of IsAddUnit.
- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 215 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 6 definitions · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
Cited by226
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.map_addUnitsstatement · cited by 36
- IsAddUnit.addUnitstatement and proof · cited by 30
- IsAddUnit.liftRightstatement and proof · cited by 25
- AddSubmonoid.LocalizationMap.liftstatement and proof · cited by 23
- IsAddUnit.addSubmonoidproof · cited by 16
- IsAddUnit.mapstatement and proof · cited by 16
- AddSubmonoid.LocalizationMap.add_neg_leftstatement and proof · cited by 15
- AddUnits.isAddUnitstatement · cited by 14
- AddGroup.isAddUnitstatement · cited by 11
- IsAddUnit.addstatement and proof · cited by 11
- IsAddUnit.addUnit'statement and proof · cited by 11
- AddSubmonoid.LocalizationMap.lift_eqstatement and proof · cited by 8
Showing the 200 most cited of 226.