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Theorems · Definition · order theory

IsWeakAntichain

{ι : Type u_1} → {α : ι → Type u_2} → [(i : ι) → Preorder (α i)] → Set ((i : ι) → α i) → Prop

A weak antichain in Π i, α i is a set such that no two distinct elements are strongly less than each other.

Defined in
Mathlib.Order.Antichain
Cited by
6 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isWeakAntichain_insert · cited by 0isWeakAntichain_insertIsAntichain.isWeakAntichain · cited by 0IsAntichain.isWeakAnticha…IsWeakAntichain.eq · cited by 0IsWeakAntichain.eqIsWeakAntichain.insert · cited by 0IsWeakAntichain.insertIsWeakAntichain.subset · cited by 0IsWeakAntichain.subsetSet.Subsingleton.isWeakAntichain · cited by 0Subsingleton.isWeakAntich…Set · cited by 53352SetPreorder · cited by 7952PreorderIsAntichain · cited by 105IsAntichainStrongLT · cited by 34StrongLTIsWeakAntichainCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.