Theorems · Theorem · group theory
Subgroup.exists_finset_card_le_mul
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [H.FiniteIndex] {S : Finset G},
Subgroup.closure ↑S = ⊤ → ∃ T, T.card ≤ H.index * S.card ∧ Subgroup.closure ↑T = ⊤- Defined in
- Mathlib.GroupTheory.Schreier
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.FiniteIndex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Fintypeproof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Finset.cardstatement and proof · cited by 2,327
- HasQuotient.Quotientproof · cited by 2,301
- Fintype.cardproof · cited by 1,386
- Finset.imageproof · cited by 910
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.rank_le_index_mul_rankproof · cited by 1