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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, 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 = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))

Detailed syntax breakdown of Definition df-chsup
StepHypRef Expression
1 chsup 30954 . 2 class
2 vx . . 3 setvar 𝑥
3 chba 30939 . . . . 5 class
43cpw 4599 . . . 4 class 𝒫 ℋ
54cpw 4599 . . 3 class 𝒫 𝒫 ℋ
62cv 1538 . . . . . 6 class 𝑥
76cuni 4906 . . . . 5 class 𝑥
8 cort 30950 . . . . 5 class
97, 8cfv 6560 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 6560 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 5224 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1539 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  31354
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