Theorems · Theorem · order theory
wellQuasiOrdered_iff_exists_monotone_subseq
∀ {α : Type u_1} {r : α → α → Prop} [IsPreorder α r],
WellQuasiOrdered r ↔ ∀ (f : ℕ → α), ∃ g, ∀ (m n : ℕ), m ≤ n → r (f (g m)) (f (g n))- Defined in
- Mathlib.Order.WellQuasiOrder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- OrderEmbeddingstatement and proof · cited by 619
- OrderEmbedding.strictMonoproof · cited by 26
- IsPreorderstatement and proof · cited by 20
- WellQuasiOrderedstatement and proof · cited by 15
- WellQuasiOrdered.exists_monotone_subseqproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Set.partiallyWellOrderedOn_iff_exists_monotone_subseqproof · cited by 2
- WellQuasiOrdered.piproof · cited by 0