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Mathlib/Algebra/Order/BigOperators/Group Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -564,16 +564,19 @@ end Finset
564564
565565namespace Fintype
566566section OrderedCommMonoid
567- variable [Fintype ι] [CommMonoid M] [PartialOrder M] [IsOrderedMonoid M] {f : ι → M}
567+ variable [Fintype ι] [CommMonoid M] [PartialOrder M] {f : ι → M}
568568
569569@ [to_additive (attr := mono) sum_mono]
570- theorem prod_mono' : Monotone fun f : ι → M ↦ ∏ i, f i := fun _ _ hfg ↦
570+ theorem prod_mono' [IsOrderedMonoid M] : Monotone fun f : ι → M ↦ ∏ i, f i := fun _ _ hfg ↦
571571 Finset.prod_le_prod' fun x _ ↦ hfg x
572572
573573@ [to_additive sum_nonneg]
574- lemma one_le_prod (hf : 1 ≤ f) : 1 ≤ ∏ i, f i := Finset.one_le_prod' fun _ _ ↦ hf _
574+ lemma one_le_prod [MulLeftMono M] (hf : 1 ≤ f) : 1 ≤ ∏ i, f i := Finset.one_le_prod' fun _ _ ↦ hf _
575575
576- @[to_additive] lemma prod_le_one (hf : f ≤ 1 ) : ∏ i, f i ≤ 1 := Finset.prod_le_one' fun _ _ ↦ hf _
576+ @[to_additive] lemma prod_le_one [MulLeftMono M] (hf : f ≤ 1 ) : ∏ i, f i ≤ 1 :=
577+ Finset.prod_le_one' fun _ _ ↦ hf _
578+
579+ variable [IsOrderedMonoid M]
577580
578581@[to_additive]
579582lemma prod_eq_one_iff_of_one_le (hf : 1 ≤ f) : ∏ i, f i = 1 ↔ f = 1 :=
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