Theorems · Theorem · number theory
Nat.factoredNumbers_compl
∀ {N : ℕ} {s : Finset ℕ}, N.primesBelow ⊆ s → (Nat.factoredNumbers s)ᶜ \ {0} ⊆ {n | N ≤ n}The non-zero non-s-factored numbers are ≥ N when s contains all primes less than N.
- Defined in
- Mathlib.NumberTheory.SmoothNumbers
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Set.ofPredstatement · cited by 6,101
- LE.le.transproof · cited by 3,151
- Compl.complstatement and proof · cited by 2,925
- Nat.primeFactorsListproof · cited by 105
- Nat.primesBelowstatement and proof · cited by 43
- Nat.factoredNumbersstatement and proof · cited by 33
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- Nat.mem_primesBelowproof · cited by 3
- Nat.le_of_mem_primeFactorsListproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- EulerProduct.norm_tsum_factoredNumbers_sub_tsum_ltproof · cited by 2
- Nat.smoothNumbers_complproof · cited by 0