Theorems · Definition · combinatorics
Cycle.next
{α : Type u_1} → [DecidableEq α] → (s : Cycle α) → s.Nodup → (x : α) → x ∈ s → αGiven a s : Cycle α such that Nodup s, retrieve the next element after x ∈ s.
- Defined in
- Mathlib.Data.List.Cycle
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 74 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cyclestatement and proof · cited by 79
- Cycle.Nodupstatement and proof · cited by 28
- List.nextproof · cited by 22
Cited by10
Results whose statement or proof uses this declaration.
- Cycle.next_memstatement · cited by 2
- Cycle.next.congr_simpstatement and proof · cited by 1
- Cycle.next_reverse_eq_prevstatement · cited by 1
- Cycle.prev_reverse_eq_nextstatement · cited by 1
- Equiv.Perm.toCycle_nextstatement and proof · cited by 0
- Cycle.formPerm_apply_mem_eq_nextstatement · cited by 0
- Cycle.next_prevstatement · cited by 0
- Cycle.next_reverse_eq_prev'statement · cited by 0
- Cycle.prev_nextstatement · cited by 0
- Cycle.prev_reverse_eq_next'statement · cited by 0