Theorems · Definition · group theory
AddSubgroup.ofAddUnits
{M : Type u_1} → [inst : AddMonoid M] → AddSubgroup (AddUnits M) → AddSubmonoid MAn additive subgroup of additive units represented as an additive submonoid of M.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddUnitsstatement and proof · cited by 325
- AddSubmonoid.mapproof · cited by 99
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddUnits.coeHomproof · cited by 15
Cited by34
Results whose statement or proof uses this declaration.
- ofAddUnits_addUnits_gcstatement · cited by 11
- ofAddUnits_addUnits_gcistatement · cited by 9
- AddSubgroup.addUnit_of_mem_ofAddUnitsstatement and proof · cited by 4
- AddSubgroup.addUnit_eq_addUnit_of_mem_ofAddUnitsstatement and proof · cited by 1
- AddSubgroup.addUnit_mem_of_mem_ofAddUnitsstatement and proof · cited by 1
- AddSubgroup.addUnit_of_mem_ofAddUnits_spec_memstatement and proof · cited by 1
- AddSubgroup.mem_ofAddUnitsstatement · cited by 1
- AddSubgroup.mem_ofAddUnits_iffstatement · cited by 1
- AddSubgroup.mem_ofAddUnits_iff_toAddUnits_memstatement · cited by 1
- AddSubgroup.mem_ofAddUnits_of_isAddUnit_of_addUnit_memstatement · cited by 1
- AddSubgroup.mem_of_mem_val_ofAddUnitsstatement and proof · cited by 1
- AddSubgroup.isAddUnit_of_mem_ofAddUnitsstatement and proof · cited by 1