Theorems · Theorem · group theory
AddSubgroup.exists_nsmul_mem_of_index_ne_zero
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, H.index ≠ 0 → ∀ (a : G), ∃ n, 0 < n ∧ n ≤ H.index ∧ n • a ∈ H- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Finiteproof · cited by 3,029
- HasQuotient.Quotientproof · cited by 2,301
- Set.Iccproof · cited by 1,702
- add_commproof · cited by 1,535
- one_ne_zeroproof · cited by 885
- Nat.cardproof · cited by 844
- QuotientAddGroup.mkproof · cited by 348
- Finset.Iccproof · cited by 348
- Nat.card_eq_fintype_cardproof · cited by 200
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.nsmul_mem_of_index_ne_zero_of_dvdproof · cited by 1
- AddSubgroup.exists_nsmul_mem_of_relIndex_ne_zeroproof · cited by 0