Definition df-chsup 31331

Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 31430 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 31359. (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 30954	. 2 class ∨ℋ
2		vx	. . 3 setvar 𝑥
3		chba 30939	. . . . 5 class ℋ
4	3	cpw 4599	. . . 4 class 𝒫 ℋ
5	4	cpw 4599	. . 3 class 𝒫 𝒫 ℋ
6	2	cv 1538	. . . . . 6 class 𝑥
7	6	cuni 4906	. . . . 5 class ∪ 𝑥
8		cort 30950	. . . . 5 class ⊥
9	7, 8	cfv 6560	. . . 4 class (⊥‘∪ 𝑥)
10	9, 8	cfv 6560	. . 3 class (⊥‘(⊥‘∪ 𝑥))
11	2, 5, 10	cmpt 5224	. 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))
12	1, 11	wceq 1539	1 wff ∨ℋ = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘∪ 𝑥)))

This definition is referenced by:  hsupval  31354