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Mathlib/Data/Set/Finite/Lattice.lean

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -389,8 +389,8 @@ theorem iUnion_univ_pi_of_monotone {ι ι' : Type*} [LinearOrder ι'] [Nonempty
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⋃ j : ι', pi univ (fun i => s i j) = pi univ fun i => ⋃ j, s i j :=
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iUnion_pi_of_monotone finite_univ fun i _ => hs i
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theorem Finite.iInf_iSup_eq {ι} {κ : ι → Sort*} [Nonempty (∀ a, κ a)] [Order.Frame α]
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{s : Set ι} (hs : s.Finite) {f : ∀ a, κ a → α} :
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theorem Finite.iInf_iSup_eq {ι} {κ : ι → Sort*} [Nonempty (∀ a, κ a)] [Order.Frame α] {s : Set ι}
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(hs : s.Finite) {f : ∀ a, κ a → α} :
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⨅ a ∈ s, ⨆ b, f a b = ⨆ g : ∀ a, κ a, ⨅ a ∈ s, f a (g a) := by
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classical
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induction s, hs using Set.Finite.induction_on with
@@ -405,8 +405,8 @@ theorem Finite.iInf_iSup_eq {ι} {κ : ι → Sort*} [Nonempty (∀ a, κ a)] [O
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exact ha ha'
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· exact le_iSup_of_le (g a) (le_iSup_of_le g le_rfl)
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theorem Finite.iSup_iInf_eq {ι} {κ : ι → Sort*} [Nonempty (∀ a, κ a)] [Order.Coframe α]
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{s : Set ι} (hs : s.Finite) {f : ∀ a, κ a → α} :
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theorem Finite.iSup_iInf_eq {ι} {κ : ι → Sort*} [Nonempty (∀ a, κ a)] [Order.Coframe α] {s : Set ι}
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(hs : s.Finite) {f : ∀ a, κ a → α} :
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⨆ a ∈ s, ⨅ b, f a b = ⨅ g : ∀ a, κ a, ⨆ a ∈ s, f a (g a) := by
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classical
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induction s, hs using Set.Finite.induction_on with

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