Theorems · Theorem · group theory
AddSubgroup.mem_ofAddUnits
∀ {M : Type u_1} [inst : AddMonoid M] (S : AddSubgroup (AddUnits M)) {x : M} {y : AddUnits M},
y ∈ S → ↑y = x → x ∈ S.ofAddUnits- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 1 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 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.valstatement and proof · cited by 248
- AddSubgroup.ofAddUnitsstatement · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_ofAddUnits_of_isAddUnit_of_addUnit_memproof · cited by 1