Theorems · Theorem · group theory

finprod_nonneg

∀ {α : Sort u_4} {R : Type u_7} [inst : CommMonoidWithZero R] [inst_1 : Preorder R] [ZeroLEOneClass R] [PosMulMono R]
  {f : α → R}, (∀ (x : α), 0 ≤ f x) → 0 ≤ ∏ᶠ (x : α), f x

Defined in

Mathlib.Algebra.BigOperators.Finprod

Cited by

6 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroPreorderZeroLEOneClassPosMulMono