Theorems · Theorem · group theory
MulAction.index_stabilizer
∀ (G : Type u_1) {X : Type u_2} [inst : Group G] [inst_1 : MulAction G X] (x : X),
(MulAction.stabilizer G x).index = (MulAction.orbit G x).ncard- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Set.ncardstatement · cited by 344
- MulAction.stabilizerstatement · cited by 254
- Subgroup.indexstatement · cited by 150
- Nat.card_congrproof · cited by 133
- MulAction.orbitstatement and proof · cited by 114
- Nat.card_coe_set_eqproof · cited by 19
- MulAction.orbitEquivQuotientStabilizerproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.ncard_block_mul_ncard_orbit_eqproof · cited by 4
- MulAction.index_stabilizer_of_transitiveproof · cited by 2
- MulAction.IsBlock.ncard_block_eq_relIndexproof · cited by 1
- Ideal.ncard_primesOver_mul_ncard_primesOverproof · cited by 0