Theorems · Theorem · order theory
Set.IsPWO.exists_monotone_subseq
∀ {α : Type u_2} [inst : Preorder α] {s : Set α}, s.IsPWO → ∀ {f : ℕ → α}, (∀ (n : ℕ), f n ∈ s) → ∃ g, Monotone (f ∘ ⇑g)- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- OrderEmbeddingstatement · cited by 619
- Set.IsPWOstatement and proof · cited by 99
- Set.PartiallyWellOrderedOn.exists_monotone_subseqproof · cited by 9
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