Theorems · Theorem · group theory
MulAction.orbitRel.Quotient.mem_orbit
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {a : α} {x : MulAction.orbitRel.Quotient G α},
a ∈ x.orbit ↔ Quotient.mk'' a = x- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 68 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
- MulActionstatement and proof · cited by 1,294
- Quotient.mk''statement and proof · cited by 132
- MulAction.orbitRelstatement · cited by 114
- Quotient.inductionOn'proof · cited by 69
- Quotient.eq''proof · cited by 44
- MulAction.orbitRel.Quotientstatement and proof · cited by 28
- MulAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- QuotientGroup.orbit_mk_eq_smulproof · cited by 1
- MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff'proof · cited by 0