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Theorems · Theorem · order theory

Multiset.prod_nonneg

∀ {R : Type u_1} [inst : CommMonoidWithZero R] [inst_1 : PartialOrder R] [ZeroLEOneClass R] [PosMulMono R]
  {s : Multiset R}, (∀ a ∈ s, 0 ≤ a) → 0 ≤ s.prod
Defined in
Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
CommMonoidWithZeroPartialOrderZeroLEOneClassPosMulMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Multiset.prod_map_nonneg · cited by 4Multiset.prod_map_nonnegPartialOrder · cited by 6410PartialOrderMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.prod · cited by 528Multiset.prodZeroLEOneClass · cited by 304ZeroLEOneClassPosMulMono · cited by 165PosMulMonoList.prod_nonneg · cited by 1List.prod_nonnegMultiset.prod_nonnegCITED BYCITES

Cites7

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Cited by1

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