Theorems · Theorem · group theory
zsmul_mem
∀ {M : Type u_3} {S : Type u_4} [inst : SubNegMonoid M] [inst_1 : SetLike S M] [hSM : AddSubgroupClass S M] {K : S}
{x : M}, x ∈ K → ∀ (n : ℤ), n • x ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement and proof · cited by 1,084
- AddSubgroupClassstatement and proof · cited by 240
- natCast_zsmulproof · cited by 118
- SubNegMonoidstatement and proof · cited by 79
- NegMemClass.neg_memproof · cited by 63
- negSucc_zsmulproof · cited by 45
- nsmul_memproof · cited by 26
Cited by14
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_closure_singletonproof · cited by 6
- ZLattice.rankproof · cited by 5
- AddSubgroup.zsmul_memproof · cited by 3
- AddSubgroup.dense_of_not_isolated_zeroproof · cited by 2
- Subalgebra.zsmul_memproof · cited by 1
- AddSubgroup.mem_closure_range_iffproof · cited by 1
- zmod_smul_memproof · cited by 1
- AddSubgroupClass.zsmulMemClassproof · cited by 1
- TwoSidedIdeal.zsmul_memproof · cited by 0
- NonUnitalSubring.zsmul_memproof · cited by 0
- Subring.zsmul_memproof · cited by 0
- ZMod.smul_memproof · cited by 0