Theorems · Definition · group theory
Subgroup.unit_of_mem_ofUnits
{M : Type u_1} → [inst : Monoid M] → (S : Subgroup Mˣ) → {x : M} → x ∈ S.ofUnits → MˣGiven some x : M which is a member of the submonoid of 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
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement and proof · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- Subgroup.ofUnitsstatement and proof · cited by 31
- Units.copyproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.unit_eq_unit_of_mem_ofUnitsstatement · cited by 1
- Subgroup.unit_of_mem_ofUnits_spec_memstatement · cited by 1
- Subgroup.ofUnitsEquivTypeproof · cited by 0
- Subgroup.unit_of_mem_ofUnits_spec_eq_of_val_memstatement · cited by 0
- Subgroup.unit_of_mem_ofUnits_spec_val_eq_of_memstatement · cited by 0