Theorems · Theorem · number theory
Prime.dvd_prod_iff
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p : M} {L : List M}, Prime p → (p ∣ L.prod ↔ ∃ a ∈ L, p ∣ a)Prime p divides the product of a list L iff it divides some a ∈ L
- Defined in
- Mathlib.Data.List.Prime
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
- dvd_transproof · cited by 50
- Prime.dvd_or_dvdproof · cited by 17
- Prime.not_dvd_oneproof · cited by 6
- List.dvd_prodproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- mem_list_primes_of_dvd_prodproof · cited by 2
- Prime.not_dvd_prodproof · cited by 0