Theorems · Theorem · group theory
AddAction.mem_orbit
∀ {γ : Type u_2} {α : Type u_3} [inst : VAdd γ α] (a : α) (m : γ), m +ᵥ a ∈ AddAction.orbit γ a- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- VAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- HVAdd.hVAddstatement · cited by 1,820
- VAddstatement and proof · cited by 616
- AddAction.orbitstatement · cited by 86
Cited by14
Results whose statement or proof uses this declaration.
- AddAction.quotient_preimage_image_eq_union_addproof · cited by 3
- AddAction.orbit_addSubmonoid_subsetproof · cited by 3
- AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iffproof · cited by 2
- AddAction.mem_orbit_of_mem_orbitproof · cited by 2
- AddAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPointsproof · cited by 1
- AddAction.orbit_vadd_subsetproof · cited by 1
- AddAction.snd_mem_orbit_of_mem_orbitproof · cited by 1
- AddAction.subsingleton_orbit_iff_mem_fixedPointsproof · cited by 1
- AddAction.fst_mem_orbit_of_mem_orbitproof · cited by 1
- AddAction.mem_addSubgroup_orbit_iffproof · cited by 0
- AddAction.mem_fixedPoints'proof · cited by 0
- AddAction.vadd_mem_orbit_vaddproof · cited by 0