Theorems · Theorem · group theory
AddSubgroup.rank_closure_finite_le_nat_card
∀ {G : Type u_1} [inst : AddGroup G] (s : Set G) [inst_1 : Finite ↑s],
AddGroup.rank ↥(AddSubgroup.closure s) ≤ Nat.card ↑s- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- 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
- AddSubgroup.closurestatement and proof · cited by 156
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