Theorems · Definition · group theory
Submonoid.unitsEquivIsUnitSubmonoid
{M : Type u_1} → [inst : Monoid M] → (S : Submonoid M) → ↥S.units ≃* ↥(IsUnit.submonoid ↥S)The equivalence between the subgroup of units of S and the submonoid of unit
elements of S.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement · cited by 3,593
- Submonoidstatement and proof · cited by 3,086
- Unitsstatement · cited by 2,804
- MulEquivstatement · cited by 1,142
- IsUnit.submonoidstatement · cited by 56
- MulEquiv.transproof · cited by 53
- Submonoid.unitsstatement · cited by 40
- Submonoid.unitsEquivUnitsTypeproof · cited by 8
- Submonoid.unitsTypeEquivIsUnitSubmonoidproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.