Theorems · Theorem · number theory
Nat.mem_primesBelow
∀ {k n : ℕ}, n ∈ k.primesBelow ↔ n < k ∧ Nat.Prime n- Defined in
- Mathlib.NumberTheory.PrimeCounting
- Cited by
- 3 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.
Cites3
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 and proof · cited by 2,059
- Nat.primesBelowstatement · cited by 43
Cited by3
Results whose statement or proof uses this declaration.
- Nat.factoredNumbers_complproof · cited by 2
- Nat.eq_prod_primes_mul_sq_of_mem_smoothNumbersproof · cited by 1
- Nat.smoothNumbers_eq_factoredNumbers_primesBelowproof · cited by 1