Theorems · Theorem · order theory

Finset.prod_le_prod_of_subset_of_one_le

∀ {ι : Type u_1} {R : Type u_2} [inst : CommMonoidWithZero R] [inst_1 : Preorder R] [ZeroLEOneClass R] [PosMulMono R]
  {f : ι → R} {s t : Finset ι}, s ⊆ t → (∀ i ∈ s, 0 ≤ f i) → (∀ i ∈ t, i ∉ s → 1 ≤ f i) → ∏ i ∈ s, f i ≤ ∏ i ∈ t, f i

Defined in

Mathlib.Algebra.Order.BigOperators.GroupWithZero.Finset

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroPreorderZeroLEOneClassPosMulMono