Theorems · Definition · order theory
OrderEmbedding.birkhoffFinset
{α : Type u_1} → [inst : DistribLattice α] → [Fintype α] → [DecidablePred SupIrred] → α ↪o Finset { a // SupIrred a }Birkhoff's Representation Theorem. Any finite distributive lattice can be embedded in a powerset lattice.
- Defined in
- Mathlib.Order.Birkhoff
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- OrderEmbeddingstatement · cited by 619
- OrderIso.symmproof · cited by 475
- DistribLatticestatement and proof · cited by 150
- SupIrredstatement and proof · cited by 34
- RelEmbedding.transproof · cited by 27
- OrderIso.toOrderEmbeddingproof · cited by 22
- OrderEmbedding.birkhoffSetproof · cited by 6
- Fintype.finsetOrderIsoSetproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- LatticeHom.birkhoffFinsetproof · cited by 2
- LatticeHom.birkhoffFinset_injectiveproof · cited by 1
- OrderEmbedding.birkhoffFinset_infstatement · cited by 0
- OrderEmbedding.birkhoffFinset_supstatement · cited by 0
- OrderEmbedding.coe_birkhoffFinsetstatement · cited by 0