Definition df-chsup 31340

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31439 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 31368. (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 30963	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 30948	. . . . 5 class ℋ
4	3	cpw 4605	. . . 4 class 𝒫 ℋ
5	4	cpw 4605	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1536	. . . . . 6 class 𝑥
7	6	cuni 4912	. . . . 5 class ∪ 𝑥
8		cort 30959	. . . . 5 class ⊥
9	7, 8	cfv 6563	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6563	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5231	. 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  31363