Theorems · Theorem · number theory
Nat.exists_lt_card_nth_eq
∀ {p : ℕ → Prop} {x : ℕ}, p x → ∃ n, (∀ (hf : (Set.ofPred p).Finite), n < hf.toFinset.card) ∧ Nat.nth p n = x- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 3 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- 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
- Set.Infiniteproof · cited by 263
- Set.mem_ofPred_eqproof · cited by 122
- Nat.nthstatement and proof · cited by 84
- Set.finite_or_infiniteproof · cited by 23
- Nat.range_nth_of_infiniteproof · cited by 3
- Nat.exists_lt_card_finite_nth_eqproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Nat.nth_eq_sInfproof · cited by 5
- Nat.isLeast_nthproof · cited by 3
- Nat.subset_range_nthproof · cited by 1