Definition df-odu 16952

Description: Define the dual of an ordered structure, which replaces the order component of the structure with its reverse. See odubas 16956, oduleval 16954, and oduleg 16955 for its principal properties.

EDITORIAL: likely usable to simplify many lattice proofs, as it allows for duality arguments to be formalized; for instance latmass 17011. (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 16951	. 2 class ODual
2		vw	. . 3 setvar 𝑤
3		cvv 3173	. . 3 class V
4	2	cv 1474	. . . 4 class 𝑤
5		cnx 15692	. . . . . 6 class ndx
6		cple 15775	. . . . . 6 class le
7	5, 6	cfv 5804	. . . . 5 class (le‘ndx)
8	4, 6	cfv 5804	. . . . . 6 class (le‘𝑤)
9	8	ccnv 5037	. . . . 5 class ◡(le‘𝑤)
10	7, 9	cop 4131	. . . 4 class ⟨(le‘ndx), ◡(le‘𝑤)⟩
11		csts 15693	. . . 4 class sSet
12	4, 10, 11	co 6549	. . 3 class (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩)
13	2, 3, 12	cmpt 4643	. 2 class (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))
14	1, 13	wceq 1475	1 wff ODual = (𝑤 ∈ V ↦ (𝑤 sSet ⟨(le‘ndx), ◡(le‘𝑤)⟩))

This definition is referenced by:  oduval  16953