Theorems · Theorem · group theory
Subgroup.rank_closure_finset_le_card
∀ {G : Type u_1} [inst : Group G] (s : Finset G), Group.rank ↥(Subgroup.closure ↑s) ≤ s.card- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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.topproof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.rangeproof · cited by 4,705
- Subgroupstatement · cited by 3,593
- LE.le.transproof · cited by 3,151
- Finset.cardstatement and proof · cited by 2,327
- Set.InjOnproof · cited by 543
- Function.Injective.injOnproof · cited by 280
- Subtype.coe_injectiveproof · cited by 205
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.rank_closure_finite_le_nat_cardproof · cited by 2