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Definition df-odu 17351
Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 17355, oduleval 17353, and oduleg 17354 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 17410. (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 17350 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3341 . . 3 class V
42cv 1631 . . . 4 class 𝑤
5 cnx 16077 . . . . . 6 class ndx
6 cple 16171 . . . . . 6 class le
75, 6cfv 6050 . . . . 5 class (le‘ndx)
84, 6cfv 6050 . . . . . 6 class (le‘𝑤)
98ccnv 5266 . . . . 5 class (le‘𝑤)
107, 9cop 4328 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 16078 . . . 4 class sSet
124, 10, 11co 6815 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 4882 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1632 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oduval  17352
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