Theorems · Theorem · group theory
MulAction.mem_subgroup_orbit_iff
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {H : Subgroup G} {x : α}
{a b : ↑(MulAction.orbit G x)}, a ∈ MulAction.orbit (↥H) b ↔ ↑a ∈ MulAction.orbit ↥H ↑b- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- MulAction.orbitstatement and proof · cited by 114
- MulAction.mem_orbitproof · cited by 10
- MulAction.subgroup_smul_defproof · cited by 3
- MulAction.orbit.coe_smulproof · cited by 1
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