Theorems · Theorem · group theory
AddAction.orbit_eq_iff
∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {a b : α},
AddAction.orbit G a = AddAction.orbit G b ↔ a ∈ AddAction.orbit G b- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddAction.orbitstatement and proof · cited by 86
- AddAction.mem_orbit_selfproof · cited by 10
- AddAction.orbit_vaddproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddAction.orbit.eq_or_disjointproof · cited by 2
- AddAction.mem_orbit_symmproof · cited by 1
- AddAction.orbitRel.Quotient.orbit_injectiveproof · cited by 1
- AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'proof · cited by 0