Theorems · Theorem · number theory
Nat.count_iff_forall
∀ {p : ℕ → Prop} [inst : DecidablePred p] {n : ℕ}, Nat.count p n = n ↔ ∀ n' < n, p n'- Defined in
- Mathlib.Data.Nat.Count
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.cardproof · cited by 2,327
- Finset.rangeproof · cited by 1,341
- Finset.filterproof · cited by 949
- Finset.card_rangeproof · cited by 108
- Nat.countstatement · cited by 55
- Nat.count_eq_card_filter_rangeproof · cited by 14
- Finset.card_filter_eq_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Nat.count_of_forallproof · cited by 2