Theorems · Definition · combinatorics
derangements.derangementsRecursionEquiv
{α : Type u_1} → [DecidableEq α] → ↑(derangements (Option α)) ≃ (a : α) × (↑(derangements ↑{a}ᶜ) ⊕ ↑(derangements α))The set of derangements on Option α is equivalent to the union over all a : α of
"derangements on α ⊕ derangements on {a}ᶜ".
- Defined in
- Mathlib.Combinatorics.Derangements.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Compl.complstatement · cited by 2,925
- Equiv.Permstatement · cited by 1,375
- Equiv.transproof · cited by 337
- Equiv.sigmaCongrRightproof · cited by 12
- derangementsstatement · cited by 8
- derangements.atMostOneFixedPointEquivSum_derangementsproof · cited by 0
- derangements.derangementsOptionEquivSigmaAtMostOneFixedPointproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- card_derangements_fin_add_twoproof · cited by 1