Theorems · Theorem · group theory
Subgroup.unit_mem_of_mem_ofUnits
∀ {M : Type u_1} [inst : Monoid M] (S : Subgroup Mˣ) {x : M} {h₁ : IsUnit x}, x ∈ S.ofUnits → h₁.unit ∈ S- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsUnitstatement and proof · cited by 1,602
- IsUnit.unitstatement · cited by 252
- Subgroup.ofUnitsstatement and proof · cited by 31
- Subgroup.unit_eq_unit_of_mem_ofUnitsproof · cited by 1
- Subgroup.unit_of_mem_ofUnits_spec_memproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.mem_ofUnits_iff_exists_isUnitproof · cited by 0