Definition df-chsup 29094

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 29193 for its value. We actually define the supremum for an arbitrary collection of Hilbert space subsets, not just elements of the Hilbert lattice C_ℋ, to allow more general theorems. Even for general subsets the supremum still a Hilbert lattice element; see hsupcl 29122. (Contributed by NM, 9-Dec-2003.) (New usage is discouraged.)

Assertion

Ref	Expression
df-chsup	⊢ ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

Detailed syntax breakdown of Definition df-chsup

Step	Hyp	Ref	Expression
1		chsup 28717	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 28702	. . . . 5 class ℋ
4	3	cpw 4497	. . . 4 class 𝒫 ℋ
5	4	cpw 4497	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1537	. . . . . 6 class 𝑥
7	6	cuni 4800	. . . . 5 class ∪ 𝑥
8		cort 28713	. . . . 5 class ⊥
9	7, 8	cfv 6324	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6324	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5110	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1538	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  29117