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Definition df-odu 17444
Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 17448, oduleval 17446, and oduleg 17447 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 17503. (Contributed by Stefan O'Rear, 29-Jan-2015.)

Assertion
Ref Expression
df-odu ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))

Detailed syntax breakdown of Definition df-odu
StepHypRef Expression
1 codu 17443 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3385 . . 3 class V
42cv 1652 . . . 4 class 𝑤
5 cnx 16181 . . . . . 6 class ndx
6 cple 16274 . . . . . 6 class le
75, 6cfv 6101 . . . . 5 class (le‘ndx)
84, 6cfv 6101 . . . . . 6 class (le‘𝑤)
98ccnv 5311 . . . . 5 class (le‘𝑤)
107, 9cop 4374 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 16182 . . . 4 class sSet
124, 10, 11co 6878 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 4922 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1653 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oduval  17445
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