Theorems · Definition · logic and foundations
Nat.Subtype.ofNat
(s : Set ℕ) → [DecidablePred fun x => x ∈ s] → [Infinite ↑s] → ℕ → ↑s
Returns the n-th element of a set, according to the usual ordering of ℕ.
- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePredInfinite
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.
Cited by12
Results whose statement or proof uses this declaration.
- Nat.orderEmbeddingOfSetproof · cited by 5
- Nat.Subtype.orderIsoOfNatproof · cited by 4
- Nat.exists_subseq_of_forall_mem_unionproof · cited by 2
- Nat.Subtype.coe_comp_ofNat_rangestatement and proof · cited by 2
- Nat.Subtype.ofNat_rangestatement · cited by 1
- Nat.Subtype.ofNat_surjectivestatement and proof · cited by 1
- Nat.Subtype.orderIsoOfNat_applystatement and proof · cited by 0
- Nat.coe_orderEmbeddingOfSetstatement · cited by 0
- Nat.Subtype.ofNat.congr_simpstatement and proof · cited by 0
- Nat.Subtype.ofNat.eq_defstatement and proof · cited by 0
- Nat.orderEmbeddingOfSet_applystatement · cited by 0
- Nat.Subtype.denumerableproof · cited by 0