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Theorems · Theorem · logic and foundations

Set.union_nonempty

∀ {α : Type u} {s t : Set α}, (s ∪ t).Nonempty ↔ s.Nonempty ∨ t.Nonempty
Defined in
Mathlib.Data.Set.Basic
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.IsWF.min_union · cited by 1IsWF.min_unionFinset.union_nonempty · cited by 0Finset.union_nonemptySet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.union_nonemptyCITED BYCITES

Cites2

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.Nonemptystatement · cited by 2,627

Cited by2

Results whose statement or proof uses this declaration.