Theorems · Definition · number theory
Nat.count
(p : ℕ → Prop) → [DecidablePred p] → ℕ → ℕ
Count the number of naturals k < n satisfying p k.
- Defined in
- Mathlib.Data.Nat.Count
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by57
Results whose statement or proof uses this declaration.
- Nat.count_eq_card_filter_rangestatement · cited by 14
- Nat.primeCounting'proof · cited by 12
- Nat.nth_countstatement and proof · cited by 7
- Nat.count_nthstatement and proof · cited by 5
- Nat.count_monotonestatement · cited by 4
- Nat.count_nth_of_infinitestatement · cited by 3
- Nat.count_succstatement · cited by 3
- Nat.count_addstatement · cited by 2
- Nat.count_iff_forall_notstatement · cited by 2
- Nat.count_le_cardstatement · cited by 2
- Nat.count_lt_count_succ_iffstatement · cited by 2
- Nat.count_of_forallstatement · cited by 2