Theorems · Theorem · group theory
Equiv.Perm.mem_support_of_mem_noncommProd_support
∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq β] [inst_1 : Fintype β] {s : Finset α} {f : α → Equiv.Perm β}
{comm : (↑s).Pairwise (Function.onFun Commute f)} {x : β},
x ∈ (s.noncommProd f comm).support → ∃ a ∈ s, x ∈ (f a).support- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Commutestatement and proof · cited by 639
- Function.onFunstatement and proof · cited by 570
- Set.Pairwisestatement and proof · cited by 321
- Equiv.Perm.supportstatement and proof · cited by 230
- Finset.mem_insert_selfproof · cited by 128
- Finset.mem_insert_of_memproof · cited by 109
- Finset.coe_emptyproof · cited by 109
- Finset.inductionproof · cited by 108
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.OnCycleFactors.kerParam_applyproof · cited by 1