Theorems · Theorem · group theory
AddAction.mem_orbit_iff
∀ {γ : Type u_2} {α : Type u_3} [inst : VAdd γ α] {a₁ a₂ : α}, a₂ ∈ AddAction.orbit γ a₁ ↔ ∃ x, x +ᵥ a₁ = a₂- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 7 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 by7
Results whose statement or proof uses this declaration.
- AddAction.mem_orbit_of_mem_orbitproof · cited by 2
- AddAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPointsproof · cited by 1
- QuotientAddGroup.leftRel_eq_topproof · cited by 1
- QuotientAddGroup.rightRel_eq_topproof · cited by 0
- orbit_fixingAddSubgroup_compl_subsetproof · cited by 0
- AddAction.isPretransitive_iff_orbit_eq_univproof · cited by 0
- AddAction.mem_fixedPoints'proof · cited by 0