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Definition df-odu 17731
Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 17735, oduleval 17733, and oduleg 17734 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 17790. (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 17730 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3499 . . 3 class V
42cv 1529 . . . 4 class 𝑤
5 cnx 16472 . . . . . 6 class ndx
6 cple 16564 . . . . . 6 class le
75, 6cfv 6351 . . . . 5 class (le‘ndx)
84, 6cfv 6351 . . . . . 6 class (le‘𝑤)
98ccnv 5552 . . . . 5 class (le‘𝑤)
107, 9cop 4569 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 16473 . . . 4 class sSet
124, 10, 11co 7151 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 5142 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1530 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oduval  17732
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