Theorems · Definition · group theory
AddSubmonoid.addUnits
{M : Type u_1} → [inst : AddMonoid M] → AddSubmonoid M → AddSubgroup (AddUnits M)The additive units of S, packaged as an additive subgroup of AddUnits M.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddUnitsstatement and proof · cited by 325
- AddSubmonoid.comapproof · cited by 62
- AddUnits.coeHomproof · cited by 15
Cited by36
Results whose statement or proof uses this declaration.
- ofAddUnits_addUnits_gcstatement · cited by 11
- ofAddUnits_addUnits_gcistatement · cited by 9
- AddSubmonoid.addUnitsEquivAddUnitsTypestatement and proof · cited by 4
- AddSubgroup.mem_addUnits_iff_val_memstatement · cited by 1
- AddSubmonoid.mem_addUnits_iffstatement · cited by 1
- AddSubmonoid.val_addUnitsEquivAddUnitsType_apply_coestatement and proof · cited by 0
- AddSubmonoid.val_addUnitsEquivAddUnitsType_symm_apply_coestatement · cited by 0
- AddSubmonoid.val_mem_of_mem_addUnitsstatement and proof · cited by 0
- AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_apply_coestatement and proof · cited by 0
- AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_symm_apply_coestatement · cited by 0
- AddSubmonoid.mk_add_mk_neg_eq_zerostatement and proof · cited by 0
- ofAddUnits_le_iff_le_addUnitsstatement · cited by 0