Theorems · Theorem · group theory
MulAction.smul_orbit
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] (g : G) (a : α),
g • MulAction.orbit G a = MulAction.orbit G a- Defined in
- Mathlib.GroupTheory.GroupAction.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- LE.le.antisymmproof · cited by 507
- Set.image_monoproof · cited by 197
- MulAction.orbitstatement and proof · cited by 114
- smul_inv_smulproof · cited by 53
- MulAction.smul_orbit_subsetproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MulAction.IsFixedBlock.orbitproof · cited by 1
- MulAction.IsBlock.of_orbitproof · cited by 0
- MulAction.stabilizer_orbit_eqproof · cited by 0