Theorems · Theorem · group theory
MulAction.IsBlock.ncard_block_eq_relIndex
∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] [MulAction.IsPretransitive G X] {B : Set X},
MulAction.IsBlock G B → ∀ {x : X}, x ∈ B → B.ncard = (MulAction.stabilizer G x).relIndex (MulAction.stabilizer G B)- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Groupstatement and proof · cited by 6,238
- Subgroupproof · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- Set.ncardstatement and proof · cited by 344
- MulAction.stabilizerstatement and proof · cited by 254
- Subgroup.indexproof · cited by 150
- Subgroup.subgroupOfproof · cited by 122
- Subgroup.extproof · cited by 108
- Set.mulActionSetstatement · cited by 95
- MulAction.IsPretransitivestatement and proof · cited by 94
- MulAction.IsBlockstatement and proof · cited by 73
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.ncard_block_mul_ncard_orbit_eqproof · cited by 4