no goals
α : Type u_1
β : Type ?u.49199
γ : Type ?u.49202
δ : Type ?u.49205
inst✝ : CancelCommMonoidWithZero α
s✝ : Multiset (Associates α)
p : Associates α
hp : Prime p
a : Associates α
s : Multiset (Associates α)
ih : p ≤ Multiset.prod s → ∃ a, a ∈ s ∧ p ≤ a
h : p ≤ Multiset.prod (a ::ₘ s)
⊢ p ≤ a * Multiset.prod s
simpa using h