Theorems · Definition · group theory
AddSubgroup.ofAddUnitsEquivType
{M : Type u_1} → [inst : AddMonoid M] → (S : AddSubgroup (AddUnits M)) → ↥S.ofAddUnits ≃+ ↥SThe equivalence between the coercion of an additive subgroup S of
Mˣ to an additive submonoid of M and the additive subgroup itself as a type.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- AddEquivstatement · cited by 1,087
- AddUnitsstatement and proof · cited by 325
- AddUnits.valproof · cited by 248
- AddSubgroup.ofAddUnitsstatement and proof · cited by 30
- AddSubgroup.addUnit_of_mem_ofAddUnitsproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.ofAddUnitsTopEquivproof · cited by 0