Theorems · Definition · group theory
MulAction.orbitRel.Quotient.orbit
{G : Type u_1} → {α : Type u_2} → [inst : Group G] → [inst_1 : MulAction G α] → MulAction.orbitRel.Quotient G α → Set αThe orbit corresponding to an element of the quotient by MulAction.orbitRel
- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- MulActionstatement and proof · cited by 1,294
- MulAction.orbitproof · cited by 114
- MulAction.orbitRel.Quotientstatement and proof · cited by 28
- Quotient.liftOn'proof · cited by 19
Cited by18
Results whose statement or proof uses this declaration.
- MulAction.orbitRel.Quotient.orbit_eq_orbit_outstatement and proof · cited by 4
- MulAction.orbitRel.Quotient.mem_orbitstatement and proof · cited by 2
- MulAction.orbitRel.Quotient.mem_subgroup_orbit_iffstatement and proof · cited by 2
- MulAction.selfEquivSigmaOrbits'statement · cited by 1
- QuotientGroup.orbit_eq_out_smulstatement · cited by 1
- QuotientGroup.orbit_mk_eq_smulstatement · cited by 1
- MulAction.orbitRel.Quotient.orbit_injectivestatement and proof · cited by 1
- MulAction.univ_eq_iUnion_orbitstatement and proof · cited by 1
- MulAction.orbitRel.Quotient.orbit.coe_smulstatement and proof · cited by 1
- MulAction.equivSubgroupOrbitsstatement · cited by 0
- MulAction.equivSubgroupOrbitsSetoidComapstatement and proof · cited by 0
- Finite.of_finite_mulAction_orbitRel_quotientproof · cited by 0