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Definition df-chsup 28510
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 28609 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 28538. (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 28131 . 2 class
2 vx . . 3 setvar 𝑥
3 chil 28116 . . . . 5 class
43cpw 4297 . . . 4 class 𝒫 ℋ
54cpw 4297 . . 3 class 𝒫 𝒫 ℋ
62cv 1630 . . . . . 6 class 𝑥
76cuni 4574 . . . . 5 class 𝑥
8 cort 28127 . . . . 5 class
97, 8cfv 6031 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 6031 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 4863 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1631 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  28533
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