Theorems · Theorem · number theory
Nat.primeFactors_subset_of_mem_smoothNumbers
∀ {m n : ℕ}, m ∈ n.smoothNumbers → m.primeFactors ⊆ n.primesBelowThe Finset of prime factors of an n-smooth number is contained in the Finset
of primes below n.
- Defined in
- Mathlib.NumberTheory.SmoothNumbers
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Nat.primeFactorsstatement · cited by 129
- Nat.primesBelowstatement · cited by 43
- Nat.smoothNumbersstatement and proof · cited by 32
- Nat.primeFactors_subset_of_mem_factoredNumbersproof · cited by 3
- Nat.smoothNumbers_eq_factoredNumbers_primesBelowproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.mem_smoothNumbers_iff_primeFactors_subsetproof · cited by 0