Theorems · Theorem · group theory
MulAction.mem_orbit_self
∀ {M : Type u_1} {α : Type u_3} [inst : Monoid M] [inst_1 : MulAction M α] (a : α), a ∈ MulAction.orbit M a- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 9 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
- Monoidstatement and proof · cited by 3,887
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- MulAction.orbitstatement · cited by 114
Cited by9
Results whose statement or proof uses this declaration.
- MulAction.orbit_eq_iffproof · cited by 3
- mem_closure_isSwapproof · cited by 2
- MulAction.orbitZPowersEquiv_symm_applystatement · cited by 1
- RootPairing.span_orbit_eq_topproof · cited by 1
- MulAction.IsPartition.of_orbitsproof · cited by 1
- MulAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPointsproof · cited by 1
- MulAction.orbitZPowersEquiv_symm_apply'statement and proof · cited by 0
- MulAction.subsingleton_orbit_iff_mem_fixedPointsproof · cited by 0
- MulAction.stabilizer_orbit_eqproof · cited by 0