Theorems · Theorem · group theory
MulAction.mem_stabilizer_set
∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] {a : G} {s : Set α},
a ∈ MulAction.stabilizer G s ↔ ∀ (b : α), a • b ∈ s ↔ b ∈ s- Defined in
- Mathlib.Algebra.Pointwise.Stabilizer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- MulAction.stabilizerstatement · cited by 254
- Set.mulActionSetstatement · cited by 95
- smul_inv_smulproof · cited by 53
- MulAction.toPermproof · cited by 30
- MulAction.mem_stabilizer_iffproof · cited by 20
- Set.smul_mem_smul_set_iffproof · cited by 14
- Equiv.forall_congr'proof · cited by 5
- MulAction.toPerm_symm_applyproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.stabilizer_subset_div_rightproof · cited by 1