Definition df-odu 18208

Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 18212, oduleval 18210, and oduleg 18211 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 18416. (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

Step	Hyp	Ref	Expression
1		codu 18207	. 2 class ODual
2		vw	. . 3 setvar 𝑤
3		cvv 3438	. . 3 class V
4	2	cv 1540	. . . 4 class 𝑤
5		cnx 17118	. . . . . 6 class ndx
6		cple 17182	. . . . . 6 class le
7	5, 6	cfv 6490	. . . . 5 class (le‘ndx)
8	4, 6	cfv 6490	. . . . . 6 class (le‘𝑤)
9	8	ccnv 5621	. . . . 5 class ◡(le‘𝑤)
10	7, 9	cop 4584	. . . 4 class ⟨(le‘ndx), ◡(le‘𝑤)⟩
11		csts 17088	. . . 4 class sSet
12	4, 10, 11	co 7356	. . 3 class (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩)
13	2, 3, 12	cmpt 5177	. 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))
14	1, 13	wceq 1541	1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))

This definition is referenced by:  oduval  18209