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Definition df-odu 16895
Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 16899, oduleval 16897, and oduleg 16898 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 16954. (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 16894 . 2 class ODual
2 vw . . 3 setvar 𝑤
3 cvv 3169 . . 3 class V
42cv 1473 . . . 4 class 𝑤
5 cnx 15635 . . . . . 6 class ndx
6 cple 15718 . . . . . 6 class le
75, 6cfv 5787 . . . . 5 class (le‘ndx)
84, 6cfv 5787 . . . . . 6 class (le‘𝑤)
98ccnv 5024 . . . . 5 class (le‘𝑤)
107, 9cop 4127 . . . 4 class ⟨(le‘ndx), (le‘𝑤)⟩
11 csts 15636 . . . 4 class sSet
124, 10, 11co 6524 . . 3 class (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩)
132, 3, 12cmpt 4634 . 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
141, 13wceq 1474 1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), (le‘𝑤)⟩))
Colors of variables: wff setvar class
This definition is referenced by:  oduval  16896
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