Theorems · Theorem · order theory
wellQuasiOrderedLE_iff
∀ {α : Type u_1} [inst : Preorder α],
WellQuasiOrderedLE α ↔ WellFoundedLT α ∧ ∀ (s : Set α), IsAntichain (fun x1 x2 => x1 ≤ x2) s → s.FiniteA preorder is well quasi-ordered iff it's well-founded and has no infinite antichains.
- Defined in
- Mathlib.Order.WellQuasiOrder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Preorderstatement and proof · cited by 7,952
- Set.rangeproof · cited by 4,705
- Set.Finitestatement and proof · cited by 1,814
- le_rflproof · cited by 1,558
- OrderEmbeddingproof · cited by 619
- WellFoundedLTstatement and proof · cited by 491
- lt_trichotomyproof · cited by 178
- IsAntichainstatement and proof · cited by 105
- IsWellFounded.wfproof · cited by 43
- lt_of_le_not_geproof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- wellQuasiOrderedLE_iff_wellFoundedLTproof · cited by 1