Theorems · Theorem · group theory
MulAction.orbit_smul
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] (g : G) (a : α),
MulAction.orbit G (g • a) = MulAction.orbit G a- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- 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.
Cites7
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
- LE.le.antisymmproof · cited by 507
- MulAction.orbitstatement and proof · cited by 114
- inv_smul_smulproof · cited by 76
- MulAction.orbit_smul_subsetproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- MulAction.orbit_eq_iffproof · cited by 3
- MulAction.smul_mem_orbit_smulproof · cited by 0
- MulAction.mem_orbit_smulproof · cited by 0