Theorems · Theorem · group theory
MulAction.ofQuotientStabilizer_mem_orbit
∀ (G : Type u) {X : Type v} [inst : Group G] [inst_1 : MulAction G X] (x : X) (g : G ⧸ MulAction.stabilizer G x),
MulAction.ofQuotientStabilizer G x g ∈ MulAction.orbit G x- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 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.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- MulActionstatement and proof · cited by 1,294
- MulAction.stabilizerstatement and proof · cited by 254
- MulAction.orbitstatement · cited by 114
- Quotient.inductionOn'proof · cited by 69
- MulAction.ofQuotientStabilizerstatement · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.orbitEquivQuotientStabilizerproof · cited by 3