Theorems · Theorem · number theory
Nat.nth_strictMonoOn
∀ {p : ℕ → Prop} (hf : (Set.ofPred p).Finite), StrictMonoOn (Nat.nth p) (Set.Iio hf.toFinset.card)- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Iiostatement and proof · cited by 1,166
- Set.Finite.toFinsetstatement and proof · cited by 351
- StrictMonoOnstatement · cited by 194
- Nat.nthstatement · cited by 84
- Finset.orderEmbOfFinproof · cited by 47
- OrderEmbedding.strictMonoproof · cited by 26
- Nat.nth_eq_orderEmbOfFinproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Nat.nth_lt_nth_of_lt_cardproof · cited by 2
- Nat.nth_le_nth_of_lt_cardproof · cited by 2
- Nat.le_nthproof · cited by 1
- Nat.le_nth_of_lt_nth_succproof · cited by 1
- Nat.nth_injOnproof · cited by 0