Theorems · Theorem · number theory
Nat.count_nth_of_infinite
∀ {p : ℕ → Prop} [inst : DecidablePred p], (Set.ofPred p).Infinite → ∀ (n : ℕ), Nat.count p (Nat.nth p n) = n- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 94 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.
Cites6
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
- Set.Finiteproof · cited by 1,814
- Set.Infinitestatement and proof · cited by 263
- Nat.nthstatement · cited by 84
- Nat.countstatement · cited by 55
- Nat.count_nthproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Nat.surjective_count_of_infinite_setOfPredproof · cited by 2
- Nat.giCountNthproof · cited by 1
- Nat.primeCounting'_nth_eqproof · cited by 0
- Nat.count_nth_succ_of_infiniteproof · cited by 0