Theorems · Theorem · order theory
Set.inter_empty_of_inter_sUnion_empty
∀ {α : Type u_1} {s t : Set α} {S : Set (Set α)}, t ∈ S → s ∩ ⋃₀ S = ∅ → s ∩ t = ∅- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
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.sUnionstatement and proof · cited by 392
- Set.subset_sUnion_of_memproof · cited by 39
- Set.inter_subset_inter_rightproof · cited by 26
- Set.eq_empty_of_subset_emptyproof · cited by 15
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