Theorems · Definition · order theory
OrderIso.dualAntisymmetrization
(α : Type u_1) → [inst : Preorder α] → (Antisymmetrization α fun x1 x2 => x1 ≤ x2)ᵒᵈ ≃o Antisymmetrization αᵒᵈ fun x1 x2 => x1 ≤ x2
Antisymmetrization and orderDual commute.
- Defined in
- Mathlib.Order.Antisymmetrization
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement · cited by 927
- OrderIsostatement · cited by 874
- Antisymmetrizationstatement · cited by 25
- Quotient.map'proof · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- preordToPartOrdCompToDualIsoToDualCompPreordToPartOrdproof · cited by 3
- OrderIso.dualAntisymmetrization_applystatement · cited by 0
- OrderIso.dualAntisymmetrization_symm_applystatement · cited by 0
- preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coestatement · cited by 0
- preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coestatement · cited by 0
- preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe'statement · cited by 0