Theorems · Theorem · group theory
AddSubmonoid.nsmul_exponent_eq_zero
∀ {G : Type u} [inst : AddMonoid G] {S : AddSubmonoid G} {g : G}, g ∈ S → AddMonoid.exponent ↥S • g = 0- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- 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.
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoid.exponentstatement and proof · cited by 70
- AddMonoid.exponent_nsmul_eq_zeroproof · cited by 12
- ZeroMemClass.coe_eq_zeroproof · cited by 11
- AddSubmonoidClass.mk_nsmulproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.nsmul_exponent_eq_zeroproof · cited by 0