Theorems · Theorem · number theory
Nat.count_lt_card
∀ {p : ℕ → Prop} [inst : DecidablePred p] {n : ℕ} (hp : (Set.ofPred p).Finite), p n → Nat.count p n < hp.toFinset.card- Defined in
- Mathlib.Data.Nat.Count
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePred
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 · cited by 2,327
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.trans_leproof · cited by 678
- Set.Finite.toFinsetstatement · cited by 351
- Nat.countstatement · cited by 55
- Nat.count_le_cardproof · cited by 2
- Nat.count_lt_count_succ_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Nat.nth_countproof · cited by 7