Theorems · Definition · order theory
OrderEmbedding.supIrredLowerSet
{α : Type u_1} → [inst : PartialOrder α] → α ↪o { s // SupIrred s }The Birkhoff Embedding of a finite partial order as sup-irreducible elements in its lattice of lower sets.
- Defined in
- Mathlib.Order.Birkhoff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- OrderEmbeddingstatement · cited by 619
- LowerSetstatement · cited by 230
- LowerSet.Iicproof · cited by 37
- SupIrredstatement · cited by 34
- LowerSet.supIrred_Iicproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- OrderIso.supIrredLowerSetproof · cited by 3
- OrderEmbedding.supIrredLowerSet_applystatement · cited by 0
- OrderEmbedding.supIrredLowerSet_surjectivestatement · cited by 0