Theorems · Theorem · group theory
Equiv.Perm.mem_support_iff_of_commute
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {g c : Equiv.Perm α},
Commute g c → ∀ (x : α), g x ∈ c.support ↔ x ∈ c.supportIf g and c commute, then g stabilizes the support of c
- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Commutestatement and proof · cited by 639
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.mul_applyproof · cited by 38
- Equiv.apply_eq_iff_eqproof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.commute_iff'proof · cited by 2
- Equiv.Perm.mem_cycleFactorsFinset_supportproof · cited by 2