Theorems · Theorem · number theory
Nat.le_nth
∀ {p : ℕ → Prop} {n : ℕ}, (∀ (hf : (Set.ofPred p).Finite), n < hf.toFinset.card) → n ≤ Nat.nth p n- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- Finset.cardstatement and proof · cited by 2,327
- Set.Finitestatement and proof · cited by 1,814
- le_rflproof · cited by 1,558
- Set.Finite.toFinsetstatement and proof · cited by 351
- Set.Infiniteproof · cited by 263
- Nat.nthstatement · cited by 84
- Set.finite_or_infiniteproof · cited by 23
- StrictMonoOn.monoproof · cited by 15
- StrictMono.id_leproof · cited by 14
- Set.Iic_subset_Iioproof · cited by 12
- Nat.nth_strictMonoproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Nat.nth_eq_zeroproof · cited by 0