Theorems · Theorem · group theory
stabilizer_compl
∀ (G : Type u_1) [inst : Group G] (α : Type u_2) [inst_1 : MulAction G α] {s : Set α},
MulAction.stabilizer G sᶜ = MulAction.stabilizer G sThe stabilizer of the complement is the stabilizer of the set.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Compl.complstatement and proof · cited by 2,925
- le_antisymmproof · cited by 2,068
- MulActionstatement and proof · cited by 1,294
- MulAction.stabilizerstatement and proof · cited by 254
- compl_complproof · cited by 229
- Set.mulActionSetstatement · cited by 95
- MulAction.mem_stabilizer_iffproof · cited by 20
- Set.smul_set_complproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.isPretransitive_of_stabilizer_ltproof · cited by 2
- Equiv.Perm.exists_mem_stabilizer_isThreeCycleproof · cited by 2
- alternatingGroup.isCoatom_stabilizerproof · cited by 1
- Equiv.Perm.has_swap_mem_of_lt_stabilizerproof · cited by 1
- Equiv.Perm.isCoatom_stabilizerproof · cited by 1
- Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1