Theorems · Theorem · order theory
IsAntichain.finite_of_partiallyWellOrderedOn
∀ {α : Type u_2} {r : α → α → Prop} {s : Set α}, IsAntichain r s → s.PartiallyWellOrderedOn r → s.Finite- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.neproof · cited by 872
- Subtype.val_injectiveproof · cited by 232
- Function.Embedding.injectiveproof · cited by 111
- IsAntichainstatement and proof · cited by 105
- Subrelproof · cited by 53
- Set.PartiallyWellOrderedOnstatement and proof · cited by 34
- IsAntichain.eqproof · cited by 13
- Set.Infinite.natEmbeddingproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- AddSubmonoid.fg_of_subtractiveproof · cited by 2
- Submonoid.fg_of_divisiveproof · cited by 2
- AddSemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0
- IsAntichain.partiallyWellOrderedOn_iffproof · cited by 0
- SemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0
- Set.partiallyWellOrderedOn_iff_finite_antichainsproof · cited by 0