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Theorems · Theorem · order theory

Multiset.prod_map_lt_prod_map

∀ {R : Type u_1} [inst : CommMonoidWithZero R] [inst_1 : PartialOrder R] [ZeroLEOneClass R] [PosMulStrictMono R]
  [NeZero 1] {ι : Type u_3} {s : Multiset ι},
  s ≠ 0 → ∀ (f g : ι → R), (∀ i ∈ s, 0 < f i) → (∀ i ∈ s, f i < g i) → (Multiset.map f s).prod < (Multiset.map g s).prod
Defined in
Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset
Cited by
0 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroPartialOrderZeroLEOneClassPosMulStrictMonoNeZero
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PartialOrder · cited by 6410PartialOrderMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroMultiset.map · cited by 876Multiset.mapMultiset.prod · cited by 528Multiset.prodZeroLEOneClass · cited by 304ZeroLEOneClassPosMulStrictMono · cited by 151PosMulStrictMonoList.prod_map_lt_prod_map · cited by 1List.prod_map_lt_prod_mapMultiset.prod_map_lt_prod_mapCITED BYCITES

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