Definition df-chsup 31918

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 32017 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 31946. (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 31541	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 31526	. . . . 5 class ℋ
4	3	cpw 4556	. . . 4 class 𝒫 ℋ
5	4	cpw 4556	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1568	. . . . . 6 class 𝑥
7	6	cuni 4866	. . . . 5 class ∪ 𝑥
8		cort 31537	. . . . 5 class ⊥
9	7, 8	cfv 6538	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6538	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5185	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1569	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is used by:  hsupval  31941