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Definition df-chsup 29073
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 29172 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 29101. (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 28696 . 2 class
2 vx . . 3 setvar 𝑥
3 chba 28681 . . . . 5 class
43cpw 4512 . . . 4 class 𝒫 ℋ
54cpw 4512 . . 3 class 𝒫 𝒫 ℋ
62cv 1537 . . . . . 6 class 𝑥
76cuni 4811 . . . . 5 class 𝑥
8 cort 28692 . . . . 5 class
97, 8cfv 6328 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 6328 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 5119 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1538 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  29096
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