Theorems · Theorem · group theory

finprod_cond_nonneg

∀ {α : Type u_1} {R : Type u_7} [inst : CommSemiring R] [inst_1 : PartialOrder R] [IsOrderedRing R] {p : α → Prop}
  {f : α → R}, (∀ (x : α), p x → 0 ≤ f x) → 0 ≤ ∏ᶠ (x : α) (_ : p x), f x

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsOrderedRing