Theorems · Theorem · group theory
AddSubgroup.exists_finset_card_le_add
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G) [H.FiniteIndex] {S : Finset G},
AddSubgroup.closure ↑S = ⊤ → ∃ T, T.card ≤ H.index * S.card ∧ AddSubgroup.closure ↑T = ⊤- Defined in
- Mathlib.GroupTheory.Schreier
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- 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
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