Theorems · Theorem · number theory
Nat.nth_of_card_le
∀ {p : ℕ → Prop} (hf : (Set.ofPred p).Finite) {n : ℕ}, hf.toFinset.card ≤ n → Nat.nth p n = 0- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 4 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.
Cites8
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
- Set.Finite.toFinsetstatement and proof · cited by 351
- Nat.nthstatement · cited by 84
- Finset.sortproof · cited by 42
- Finset.length_sortproof · cited by 6
- List.getD_eq_defaultproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Nat.nth_eq_sInfproof · cited by 5
- Nat.nth_of_forall_notproof · cited by 1
- Nat.le_nth_of_lt_nth_succproof · cited by 1
- Nat.nth_eq_zeroproof · cited by 0