Theorems · Definition · order theory
IsAntichain
{α : Type u_1} → (α → α → Prop) → Set α → PropAn antichain is a set such that no two distinct elements are related.
- Defined in
- Mathlib.Order.Antichain
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 16 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Compl.complproof · cited by 2,925
- Set.Pairwiseproof · cited by 321
Cited by112
Results whose statement or proof uses this declaration.
- IsAntichain.eqstatement and proof · cited by 13
- IsAntichain.finite_of_partiallyWellOrderedOnstatement and proof · cited by 6
- IsWeakAntichainproof · cited by 6
- IsMaxAntichainproof · cited by 5
- setOfPred_minimal_antichainstatement · cited by 5
- IsAntichain.to_dualstatement and proof · cited by 5
- IsAntichain.image_relEmbeddingstatement and proof · cited by 4
- IsAntichain.preimage_relEmbeddingstatement and proof · cited by 4
- SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNumproof · cited by 3
- IsAntichain.flipstatement and proof · cited by 3
- IsAntichain.image_relEmbedding_iffstatement and proof · cited by 3
- IsAntichain.singletonstatement · cited by 3