Theorems · Theorem · order theory
Nat.orderEmbeddingOfSet_range
∀ (s : Set ℕ) [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s], Set.range ⇑(Nat.orderEmbeddingOfSet s) = s
- Defined in
- Mathlib.Order.OrderIsoNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement · cited by 4,705
- OrderEmbeddingstatement · cited by 619
- Infinitestatement and proof · cited by 352
- Nat.orderEmbeddingOfSetstatement · cited by 5
- Nat.Subtype.coe_comp_ofNat_rangeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- exists_increasing_or_nonincreasing_subseq'proof · cited by 1