Theorems · Theorem · number theory
Nat.nth_apply_eq_orderIsoOfNat
∀ {p : ℕ → Prop} (hf : (Set.ofPred p).Infinite) (n : ℕ), Nat.nth p n = ↑((Nat.Subtype.orderIsoOfNat (Set.ofPred p)) n)When s is an infinite set, nth agrees with Nat.Subtype.orderIsoOfNat.
- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- OrderIsostatement · cited by 874
- Set.Infinitestatement and proof · cited by 263
- Nat.nthstatement · cited by 84
- Set.Infinite.to_subtypestatement · cited by 19
- Nat.Subtype.orderIsoOfNatstatement and proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Nat.nth_eq_orderIsoOfNatproof · cited by 2