Theorems · Inductive type · group theory
AddUnits
(α : Type u) → [AddMonoid α] → Type u
Units of an AddMonoid, bundled version.
An element of an AddMonoid is a unit if it has a two-sided additive inverse.
This version bundles the inverse element so that it can be computed.
For a predicate see isAddUnit.
- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 325 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement · cited by 2,864
Cited by379
Results whose statement or proof uses this declaration.
- AddUnits.valstatement and proof · cited by 248
- IsAddUnitproof · cited by 215
- AddSubmonoid.addUnitsstatement and proof · cited by 32
- AddSubgroup.ofAddUnitsstatement and proof · cited by 30
- IsAddUnit.addUnitstatement · cited by 30
- AddUnits.extstatement and proof · cited by 25
- IsAddUnit.liftRightstatement · cited by 25
- AddUnits.add_negstatement and proof · cited by 19
- add_eq_zerostatement and proof · cited by 19
- AddUnits.neg_addstatement and proof · cited by 17
- IsAddConjproof · cited by 17
- AddUnits.mapstatement and proof · cited by 16
Showing the 200 most cited of 379.