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Theorems · Theorem · order theory

Set.wellFoundedOn_union

∀ {α : Type u_2} {r : α → α → Prop} [IsStrictOrder α r] {s t : Set α},
  (s ∪ t).WellFoundedOn r ↔ s.WellFoundedOn r ∧ t.WellFoundedOn r
Defined in
Mathlib.Order.WellFoundedSet
Cited by
1 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsStrictOrder
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Around this declaration

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

Set.isWF_union · cited by 0Set.isWF_unionSet · cited by 53352SetSet.subset_union_left · cited by 142Set.subset_union_leftSet.subset_union_right · cited by 123Set.subset_union_rightSet.WellFoundedOn · cited by 53Set.WellFoundedOnIsStrictOrder · cited by 28IsStrictOrderSet.WellFoundedOn.subset · cited by 3WellFoundedOn.subsetSet.WellFoundedOn.union · cited by 2WellFoundedOn.unionSet.wellFoundedOn_unionCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.