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forgot one_le_prod and prod_le_one
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Mathlib/Algebra/Order/BigOperators/Group/Finset.lean

Lines changed: 7 additions & 4 deletions
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@@ -564,16 +564,19 @@ end Finset
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namespace Fintype
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section OrderedCommMonoid
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variable [Fintype ι] [CommMonoid M] [PartialOrder M] [IsOrderedMonoid M] {f : ι → M}
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variable [Fintype ι] [CommMonoid M] [PartialOrder M] {f : ι → M}
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@[to_additive (attr := mono) sum_mono]
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theorem prod_mono' : Monotone fun f : ι → M ↦ ∏ i, f i := fun _ _ hfg ↦
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theorem prod_mono' [IsOrderedMonoid M] : Monotone fun f : ι → M ↦ ∏ i, f i := fun _ _ hfg ↦
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Finset.prod_le_prod' fun x _ ↦ hfg x
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@[to_additive sum_nonneg]
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lemma one_le_prod (hf : 1 ≤ f) : 1 ≤ ∏ i, f i := Finset.one_le_prod' fun _ _ ↦ hf _
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lemma one_le_prod [MulLeftMono M] (hf : 1 ≤ f) : 1 ≤ ∏ i, f i := Finset.one_le_prod' fun _ _ ↦ hf _
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@[to_additive] lemma prod_le_one (hf : f ≤ 1) : ∏ i, f i ≤ 1 := Finset.prod_le_one' fun _ _ ↦ hf _
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@[to_additive] lemma prod_le_one [MulLeftMono M] (hf : f ≤ 1) : ∏ i, f i ≤ 1 :=
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Finset.prod_le_one' fun _ _ ↦ hf _
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variable [IsOrderedMonoid M]
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@[to_additive]
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lemma prod_eq_one_iff_of_one_le (hf : 1 ≤ f) : ∏ i, f i = 1 ↔ f = 1 :=

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