Theorems · Theorem · group theory
AddAction.mem_orbit_self
∀ {M : Type u_1} {α : Type u_3} [inst : AddMonoid M] [inst_1 : AddAction M α] (a : α), a ∈ AddAction.orbit M a- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddMonoidstatement and proof · cited by 2,864
- AddActionstatement and proof · cited by 820
- zero_vaddproof · cited by 95
- AddAction.orbitstatement · cited by 86
Cited by10
Results whose statement or proof uses this declaration.
- AddAction.orbit_eq_iffproof · cited by 4
- AddAction.orbitZMultiplesEquiv_symm_applystatement · cited by 1
- AddAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPointsproof · cited by 1
- AddAction.univ_eq_iUnion_orbitproof · cited by 1
- AddAction.subsingleton_orbit_iff_mem_fixedPointsproof · cited by 1
- AddAction.IsPartition.of_orbitsproof · cited by 1
- AddAction.orbitZMultiplesEquiv_symm_apply'statement and proof · cited by 0
- AddAction.stabilizer_orbit_eqproof · cited by 0
- AddAction.mem_orbit_vaddproof · cited by 0
- Flow.mem_orbit_selfproof · cited by 0