Theorems · Theorem · number theory
Nat.prime_of_mem_primesLE
∀ {p n : ℕ}, p ∈ n.primesLE → Nat.Prime p- Defined in
- Mathlib.NumberTheory.PrimeCounting
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Nat.Primestatement · cited by 2,059
- Nat.primesLEstatement and proof · cited by 30
- Nat.prime_of_mem_primesBelowproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Chebyshev.psi_le_primeCounting_mul_logproof · cited by 3
- Chebyshev.psi_eq_sum_mul_log_primeproof · cited by 2
- Nat.primeFactors_lcmUptoproof · cited by 2
- Nat.lcmUpto_eq_prod_pow_logproof · cited by 2
- primeFactors_primorialproof · cited by 0
- squarefree_primorialproof · cited by 0