Theorems · Theorem · order theory
Set.biUnion_inter_of_pairwise_disjoint
∀ {α : Type u_1} {ι : Type u_9} {f : ι → Set α},
Pairwise (Function.onFun Disjoint f) → ∀ (s t : Set ι), ⋃ i ∈ s ∩ t, f i = (⋃ i ∈ s, f i) ∩ ⋃ i ∈ t, f i- Defined in
- Mathlib.Data.Set.Lattice.Image
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.iUnionstatement · cited by 2,483
- Disjointstatement and proof · cited by 2,201
- Function.onFunstatement and proof · cited by 570
- Pairwisestatement and proof · cited by 516
- biSup_inter_of_pairwise_disjointproof · cited by 1
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