Theorems · Theorem · group theory
Subgroup.rank_closure_finite_le_nat_card
∀ {G : Type u_1} [inst : Group G] (s : Set G) [inst_1 : Finite ↑s], Group.rank ↥(Subgroup.closure s) ≤ Nat.card ↑s- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Finset.cardproof · cited by 2,327
- Nat.cardstatement · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Set.toFinsetproof · cited by 217
- Nat.card_eq_fintype_cardproof · cited by 200
- Subgroup.closurestatement and proof · cited by 196
Cited by2
Results whose statement or proof uses this declaration.
- rank_closureCommutatorRepresentatives_leproof · cited by 1
- Subgroup.rank_commutator_le_cardproof · cited by 1