Theorems · Theorem · group theory
AddAction.orbitRel.Quotient.mem_orbit
∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {a : α}
{x : AddAction.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
- AddGroupstatement and proof · cited by 4,410
- AddActionstatement and proof · cited by 820
- Quotient.mk''statement and proof · cited by 132
- Quotient.inductionOn'proof · cited by 69
- AddAction.orbitRelstatement · cited by 47
- Quotient.eq''proof · cited by 44
- AddAction.orbitRel.Quotientstatement and proof · cited by 17
- AddAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- QuotientAddGroup.orbit_mk_eq_vaddproof · cited by 1
- AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'proof · cited by 0