Theorems · Definition · group theory
AddSubgroup.addUnit_of_mem_ofAddUnits
{M : Type u_1} → [inst : AddMonoid M] → (S : AddSubgroup (AddUnits M)) → {x : M} → x ∈ S.ofAddUnits → AddUnits MGiven some x : M which is a member of the additive submonoid of additive unit
elements corresponding to a subgroup of units, produce a unit of M whose coercion is equal to
x.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice
- 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
- AddUnits.valproof · cited by 248
- AddSubgroup.ofAddUnitsstatement and proof · cited by 30
- AddUnits.copyproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.addUnit_of_mem_ofAddUnits_spec_memstatement · cited by 1
- AddSubgroup.addUnit_eq_addUnit_of_mem_ofAddUnitsstatement · cited by 1
- AddSubgroup.addUnit_of_mem_ofAddUnits_spec_val_eq_of_memstatement · cited by 0
- AddSubgroup.ofAddUnitsEquivTypeproof · cited by 0
- AddSubgroup.addUnit_of_mem_ofAddUnits_spec_eq_of_val_memstatement · cited by 0