Definition df-chsup 29088

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 29187 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 29116. (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 28711	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 28696	. . . . 5 class ℋ
4	3	cpw 4539	. . . 4 class 𝒫 ℋ
5	4	cpw 4539	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1536	. . . . . 6 class 𝑥
7	6	cuni 4838	. . . . 5 class ∪ 𝑥
8		cort 28707	. . . . 5 class ⊥
9	7, 8	cfv 6355	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6355	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5146	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1537	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  29111