Theorems · Theorem · order theory
iSup_iInf_eq_of_finite
∀ {α : Type u} {ι : Sort v} {κ : ι → Sort w} [inst : Order.Coframe α] [Finite ι] {f : (a : ι) → κ a → α},
⨆ a, ⨅ b, f a b = ⨅ g, ⨆ a, f a (g a)- Defined in
- Mathlib.Data.Set.Finite.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.CoframeFinite
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- iInfstatement · cited by 1,690
- Order.Coframestatement and proof · cited by 38
- iInf_iSup_eq_of_finiteproof · cited by 2
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