Theorems · Theorem · group theory
Subgroup.IsComplement.encard_left
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {S : Set G} [H.FiniteIndex],
Subgroup.IsComplement S ↑H → S.encard = ↑H.index- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.FiniteIndex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- ENatstatement and proof · cited by 4,985
- Subgroupstatement and proof · cited by 3,593
- Set.encardstatement · cited by 327
- Subgroup.indexstatement and proof · cited by 150
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Subgroup.IsComplementstatement and proof · cited by 94
- Set.Finite.cast_ncard_eqproof · cited by 28
- Subgroup.IsComplement.finite_leftproof · cited by 1
- Subgroup.IsComplement.ncard_leftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Subgroup.index_mul_measureproof · cited by 0