Theorems · Theorem · order theory

Multiset.le_prod_of_submultiplicative_on_pred_of_nonneg

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : CommMonoidWithZero β] [inst_2 : PartialOrder β]
  [PosMulMono β] (f : α → β) (p : α → Prop),
  (∀ (a : α), 0 ≤ f a) →
    f 1 ≤ 1 →
      (∀ (a b : α), p a → p b → f (a * b) ≤ f a * f b) →
        (∀ (a b : α), p a → p b → p (a * b)) → ∀ (s : Multiset α), (∀ a ∈ s, p a) → f s.prod ≤ (Multiset.map f s).prod

Defined in

Mathlib.Algebra.Order.BigOperators.Ring.Multiset

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidWithZeroPartialOrderPosMulMono