Theorems · Theorem · order theory
exists_sUnion
∀ {α : Type u_1} {S : Set (Set α)} {p : α → Prop}, (∃ x ∈ ⋃₀ S, p x) ↔ ∃ s ∈ S, ∃ x ∈ s, p x- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites4
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
- iSupproof · cited by 2,415
- Set.sUnionstatement · cited by 392
- iSup_sUnionproof · cited by 1
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