Theorems · Theorem · number theory
Nat.infinite_setOfPred_prime
{p | Nat.Prime p}.InfiniteA version of Nat.exists_infinite_primes using the Set.Infinite predicate.
- Defined in
- Mathlib.Data.Nat.PrimeFin
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement · cited by 6,101
- Nat.Primestatement · cited by 2,059
- Set.Infinitestatement · cited by 263
- Set.infinite_of_not_bddAboveproof · cited by 2
- Nat.not_bddAbove_setOfPred_primeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Nat.surjective_primeCounting'proof · cited by 2
- Nat.prime_nth_primeproof · cited by 0
- Nat.primeCounting'_nth_eqproof · cited by 0
- Nat.infinite_setOf_primeproof · cited by 0
- Nat.add_two_le_nth_primeproof · cited by 0