Theorems · Theorem · group theory
MulAction.op_smul_set_stabilizer_subset
∀ {G : Type u_1} [inst : Group G] {a : G} {s : Set G}, a ∈ s → MulOpposite.op a • ↑(MulAction.stabilizer G s) ⊆ s- Defined in
- Mathlib.Algebra.Pointwise.Stabilizer
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- MulOppositestatement · cited by 1,135
- Set.smulSetstatement · cited by 608
- MulOpposite.opstatement and proof · cited by 520
- MulAction.stabilizerstatement and proof · cited by 254
- Set.mulActionSetstatement · cited by 95
- Set.smul_mem_smul_setproof · cited by 39
- Set.smul_set_subset_iffproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.smul_set_stabilizer_subsetproof · cited by 0