Theorems · Definition · combinatorics
Cycle.nil
{α : Type u_1} → Cycle αThe unique empty cycle.
- Defined in
- Mathlib.Data.List.Cycle
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cyclestatement · cited by 79
- Cycle.ofListproof · cited by 38
Cited by26
Results whose statement or proof uses this declaration.
- Cycle.induction_onstatement and proof · cited by 4
- Equiv.Perm.toCycle_eq_toListproof · cited by 4
- Cycle.Chain.impproof · cited by 2
- Cycle.chain_iff_pairwiseproof · cited by 2
- Function.periodicOrbit_chainproof · cited by 1
- Function.periodicOrbit_eq_nil_iff_not_periodic_ptstatement and proof · cited by 1
- Function.periodicOrbit_eq_nil_of_not_periodic_ptstatement · cited by 1
- Cycle.Chain.eq_nil_of_irreflstatement and proof · cited by 1
- Cycle.Chain.nilstatement · cited by 1
- Cycle.chain_of_pairwiseproof · cited by 1
- Cycle.notMem_nilstatement · cited by 1
- Cycle.reverse_nilstatement · cited by 0