Theorems · Theorem · group theory
MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {H : Subgroup G}
{x : MulAction.orbitRel.Quotient G α} {a b : ↑x.orbit}, ↑a ∈ MulAction.orbit ↥H ↑b ↔ a ∈ MulAction.orbit (↥H) b- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 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.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- MulAction.orbitstatement and proof · cited by 114
- MulAction.orbitRel.Quotientstatement and proof · cited by 28
- MulAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
- MulAction.mem_orbitproof · cited by 10
- MulAction.subgroup_smul_defproof · cited by 3
- MulAction.orbitRel.Quotient.orbit.coe_smulproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff'proof · cited by 0
- MulAction.orbitRel.Quotient.subgroup_quotient_eq_iffproof · cited by 0