Theorems · Theorem · order theory
biInf_inter_of_pairwise_codisjoint
∀ {α : Type u} [inst : Order.Coframe α] {ι : Type u_1} {f : ι → α},
Pairwise (Function.onFun Codisjoint f) → ∀ (s t : Set ι), ⨅ i ∈ s ∩ t, f i = (⨅ i ∈ s, f i) ⊔ ⨅ i ∈ t, f i- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.Coframe
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- SProd.sprodproof · cited by 1,750
- iInfstatement and proof · cited by 1,690
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- Function.onFunstatement and proof · cited by 570
- Pairwisestatement and proof · cited by 516
- le_topproof · cited by 411
- le_sup_leftproof · cited by 265
- iInf_congr_Propproof · cited by 218
- Codisjointstatement and proof · cited by 197
- sup_leproof · cited by 159
- le_iInf₂proof · cited by 67
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