Definition df-odu 18248

Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 18252, oduleval 18250, and oduleg 18251 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 18454. (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 18247	. 2 class ODual
2		vw	. . 3 setvar 𝑤
3		cvv 3447	. . 3 class V
4	2	cv 1539	. . . 4 class 𝑤
5		cnx 17163	. . . . . 6 class ndx
6		cple 17227	. . . . . 6 class le
7	5, 6	cfv 6511	. . . . 5 class (le‘ndx)
8	4, 6	cfv 6511	. . . . . 6 class (le‘𝑤)
9	8	ccnv 5637	. . . . 5 class ◡(le‘𝑤)
10	7, 9	cop 4595	. . . 4 class ⟨(le‘ndx), ◡(le‘𝑤)⟩
11		csts 17133	. . . 4 class sSet
12	4, 10, 11	co 7387	. . 3 class (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩)
13	2, 3, 12	cmpt 5188	. 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))
14	1, 13	wceq 1540	1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))

This definition is referenced by:  oduval  18249