Theorems · Theorem · group theory
AddAction.index_stabilizer_of_transitive
∀ (G : Type u_1) {X : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G X] (x : X) [AddAction.IsPretransitive G X],
(AddAction.stabilizer G x).index = Nat.card X- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 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
- AddGroupstatement and proof · cited by 4,410
- Nat.cardstatement and proof · cited by 844
- AddActionstatement and proof · cited by 820
- Set.ncardproof · cited by 344
- AddAction.stabilizerstatement · cited by 112
- AddSubgroup.indexstatement · cited by 104
- AddAction.IsPretransitivestatement and proof · cited by 56
- Set.ncard_univproof · cited by 21
- AddAction.index_stabilizerproof · cited by 3
- AddAction.orbit_eq_univproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqproof · cited by 4