Theorems · Theorem · group theory
MulAction.index_stabilizer_of_transitive
∀ (G : Type u_1) {X : Type u_2} [inst : Group G] [inst_1 : MulAction G X] (x : X) [MulAction.IsPretransitive G X],
(MulAction.stabilizer G x).index = Nat.card X- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Nat.cardstatement and proof · cited by 844
- Set.ncardproof · cited by 344
- MulAction.stabilizerstatement · cited by 254
- Subgroup.indexstatement · cited by 150
- MulAction.IsPretransitivestatement and proof · cited by 94
- Set.ncard_univproof · cited by 21
- MulAction.index_stabilizerproof · cited by 4
- MulAction.orbit_eq_univproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.ncard_block_mul_ncard_orbit_eqproof · cited by 4
- MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2