Theorems · Theorem · group theory
Equiv.Perm.swap_mem_stabilizer
∀ {α : Type u_2} [inst : DecidableEq α] {a b : α} {s : Set α},
a ∈ s → b ∈ s → Equiv.swap a b ∈ MulAction.stabilizer (Equiv.Perm α) s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement · cited by 1,375
- MulAction.stabilizerstatement · cited by 254
- Set.Subset.antisymmproof · cited by 213
- Equiv.swapstatement and proof · cited by 197
- Set.mulActionSetstatement · cited by 95
- Equiv.swap_apply_of_ne_of_neproof · cited by 39
- MulAction.mem_stabilizer_iffproof · cited by 20
- Set.subset_smul_set_iffproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.has_swap_mem_of_lt_stabilizerproof · cited by 1
- Equiv.Perm.exists_mem_stabilizer_smul_eqproof · cited by 1