Theorems · Theorem · group theory
AddSubmonoid.mem_addUnits_iff
∀ {M : Type u_1} [inst : AddMonoid M] (S : AddSubmonoid M) (x : AddUnits M), x ∈ S.addUnits ↔ ↑x ∈ S ∧ ↑(-x) ∈ S- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 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 · cited by 3,232
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- AddUnitsstatement and proof · cited by 325
- AddUnits.valstatement · cited by 248
- AddSubmonoid.addUnitsstatement · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_addUnits_iff_val_memproof · cited by 1