Theorems · Theorem · order theory
Finset.prod_nonneg
∀ {ι : Type u_1} {R : Type u_2} [inst : CommMonoidWithZero R] [inst_1 : Preorder R] [ZeroLEOneClass R] [PosMulMono R]
{f : ι → R} {s : Finset ι}, (∀ i ∈ s, 0 ≤ f i) → 0 ≤ ∏ i ∈ s, f i- Cited by
- 39 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- Finset.prodstatement · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- mul_nonnegproof · cited by 397
- zero_le_oneproof · cited by 316
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulMonostatement and proof · cited by 165
- Finset.prod_inductionproof · cited by 18
Cited by39
Results whose statement or proof uses this declaration.
- Finset.prod_le_prodproof · cited by 40
- ContinuousMultilinearMap.ratio_le_opNormproof · cited by 5
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunctionproof · cited by 4
- ContinuousMultilinearMap.norm_compContinuousLinearMap_leproof · cited by 4
- ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_leproof · cited by 3
- summable_finsetProd_of_summable_nonnegproof · cited by 3
- NumberField.mixedEmbedding.norm_nonnegproof · cited by 2
- FormalMultilinearSeries.compAlongComposition_normproof · cited by 2
- Finset.le_prod_max_oneproof · cited by 2
- Finset.prod_le_prod_of_subset_of_one_leproof · cited by 2
- ContinuousMultilinearMap.norm_iteratedFDerivComponent_leproof · cited by 1