Theorems · Definition · order theory
Nat.orderEmbeddingOfSet
(s : Set ℕ) → [Infinite ↑s] → [DecidablePred fun x => x ∈ s] → ℕ ↪o ℕ
An order embedding from ℕ to itself with a specified range
- Defined in
- Mathlib.Order.OrderIsoNat
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- InfiniteDecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- OrderEmbeddingstatement · cited by 619
- Infinitestatement and proof · cited by 352
- RelEmbedding.transproof · cited by 27
- OrderEmbedding.subtypeproof · cited by 15
- Nat.Subtype.ofNatproof · cited by 9
- RelEmbedding.natLTproof · cited by 4
- RelEmbedding.orderEmbeddingOfLTEmbeddingproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Nat.exists_subseq_of_forall_mem_unionproof · cited by 2
- exists_increasing_or_nonincreasing_subseq'proof · cited by 1
- Nat.orderEmbeddingOfSet_rangestatement · cited by 1
- Nat.coe_orderEmbeddingOfSetstatement · cited by 0
- Nat.orderEmbeddingOfSet_applystatement · cited by 0