Prime.dvd_prod_iff

theorem 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) := by sorry

The theorem states that for a given prime `p` and a list `L` in a commutative monoid with zero, `p` divides the product of the list (`L.prod`) if and only if there exists an element `a` in the list such that `p` divides `a`. In other words, a prime number dividing a product in a commutative monoid only happens when the prime number divides at least one factor in the product.

More concisely: For a prime number `p` and a list `L` in a commutative monoid with zero, `p` divides the product `L.prod` if and only if there exists an element `a` in `L` such that `p` divides `a`.