Theorems · Theorem · group theory
AddSubgroup.nsmul_subset
∀ {G : Type u_2} [inst : AddGroup G] {s : Set G} {H : AddSubgroup G} {n : ℕ}, s ⊆ ↑H → n • s ⊆ ↑H- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- SetLike.mem_coeproof · cited by 302
- ZeroMemClass.zero_memproof · cited by 162
- zero_nsmulproof · cited by 137
- succ_nsmulproof · cited by 65
- Set.NSMulstatement · cited by 42
- Set.zero_subsetproof · cited by 7
- AddSubgroup.add_subsetproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_nsmul_leproof · cited by 1
- AddSubgroup.closure_nsmul_antiproof · cited by 0