Definition df-chsup 29090

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 29189 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 29118. (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 28713	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 28698	. . . . 5 class ℋ
4	3	cpw 4541	. . . 4 class 𝒫 ℋ
5	4	cpw 4541	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1536	. . . . . 6 class 𝑥
7	6	cuni 4840	. . . . 5 class ∪ 𝑥
8		cort 28709	. . . . 5 class ⊥
9	7, 8	cfv 6357	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6357	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5148	. 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  29113