Theorems · Theorem · order theory
Set.WellFoundedOn.union
∀ {α : Type u_2} {r : α → α → Prop} [IsStrictOrder α r] {s t : Set α},
s.WellFoundedOn r → t.WellFoundedOn r → (s ∪ t).WellFoundedOn r- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsStrictOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- OrderEmbeddingproof · cited by 619
- RelEmbeddingproof · cited by 281
- Set.WellFoundedOnstatement and proof · cited by 53
- IsStrictOrderstatement and proof · cited by 28
- RelEmbedding.transproof · cited by 27
- OrderEmbedding.ltEmbeddingproof · cited by 9
- OrderEmbedding.dualproof · cited by 9
- Set.wellFoundedOn_iff_no_descending_seqproof · cited by 3
- Nat.exists_subseq_of_forall_mem_unionproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Set.IsWF.unionproof · cited by 1
- Set.wellFoundedOn_unionproof · cited by 1