Theorems · Definition · group theory
AddSubmonoid.addUnitsEquivIsAddUnitAddSubmonoid
{M : Type u_1} → [inst : AddMonoid M] → (S : AddSubmonoid M) → ↥S.addUnits ≃+ ↥(IsAddUnit.addSubmonoid ↥S)The equivalence between the additive subgroup of additive units of
S and the additive submonoid of additive unit elements of S.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubgroupstatement · cited by 3,232
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- AddEquivstatement · cited by 1,087
- AddUnitsstatement · cited by 325
- AddEquiv.transproof · cited by 53
- AddSubmonoid.addUnitsstatement · cited by 32
- IsAddUnit.addSubmonoidstatement · cited by 16
- AddSubmonoid.addUnitsEquivAddUnitsTypeproof · cited by 4
- AddSubmonoid.addUnitsTypeEquivIsAddUnitAddSubmonoidproof · cited by 3
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