Theorems · Theorem · group theory
Group.rank_le
∀ {G : Type u_1} [inst : Group G] [h : Group.FG G] {S : Finset G}, Subgroup.closure ↑S = ⊤ → Group.rank G ≤ S.card- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Finset.cardstatement · cited by 2,327
- Subgroup.closurestatement and proof · cited by 196
- Group.FGstatement and proof · cited by 40
- Group.rankstatement · cited by 20
- Nat.find_leproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Group.rank_le_of_surjectiveproof · cited by 3
- Subgroup.rank_closure_finset_le_cardproof · cited by 1
- Group.rank_eq_zeroproof · cited by 1
- Subgroup.rank_le_index_mul_rankproof · cited by 1