Theorems · Theorem · group theory
AddAction.index_stabilizer
∀ (G : Type u_1) {X : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G X] (x : X),
(AddAction.stabilizer G x).index = (AddAction.orbit G x).ncard- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 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.
- AddGroupstatement and proof · cited by 4,410
- AddActionstatement and proof · cited by 820
- Set.ncardstatement · cited by 344
- Nat.card_congrproof · cited by 133
- AddAction.stabilizerstatement · cited by 112
- AddSubgroup.indexstatement · cited by 104
- AddAction.orbitstatement and proof · cited by 86
- Nat.card_coe_set_eqproof · cited by 19
- AddAction.orbitEquivQuotientStabilizerproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqproof · cited by 4
- AddAction.IsBlock.ncard_block_eq_relIndexproof · cited by 1
- AddAction.index_stabilizer_of_transitiveproof · cited by 1