Theorems · Theorem · group theory
nsmul_mem
∀ {M : Type u_3} {A : Type u_4} [inst : AddMonoid M] [inst_1 : SetLike A M] [AddSubmonoidClass A M] {S : A} {x : M},
x ∈ S → ∀ (n : ℕ), n • x ∈ S- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- SetLikestatement and proof · cited by 1,084
- AddSubmonoidClassstatement and proof · cited by 346
Cited by26
Results whose statement or proof uses this declaration.
- zsmul_memproof · cited by 14
- AddSubmonoid.closure_singleton_eqproof · cited by 2
- NNRat.addSubmonoid_closure_range_powproof · cited by 2
- AddSubmonoid.mem_closure_finsetproof · cited by 2
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_memproof · cited by 1
- AddSubgroup.nsmul_memproof · cited by 1
- AddSubgroup.nsmul_mem_of_index_ne_zero_of_dvdproof · cited by 1
- LieAlgebra.IsKilling.coroot_mem_corootSpaceproof · cited by 1
- AddSubmonoidClass.mk_nsmulstatement · cited by 1
- AddSubmonoidClass.nsmulMemClassproof · cited by 1
- Int.addSubmonoid_closure_range_powproof · cited by 1
- IsLinearSet.closureproof · cited by 1