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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.Finite

A 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

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