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Definition df-chsup 28725
 Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 28824 for its value. We actually define the supremum for an arbitrary collection of Hilbert space subsets, not just elements of the Hilbert lattice Cℋ, to allow more general theorems. Even for general subsets the supremum still a Hilbert lattice element; see hsupcl 28753. (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 28346 . 2 class
2 vx . . 3 setvar 𝑥
3 chba 28331 . . . . 5 class
43cpw 4378 . . . 4 class 𝒫 ℋ
54cpw 4378 . . 3 class 𝒫 𝒫 ℋ
62cv 1657 . . . . . 6 class 𝑥
76cuni 4658 . . . . 5 class 𝑥
8 cort 28342 . . . . 5 class
97, 8cfv 6123 . . . 4 class (⊥‘ 𝑥)
109, 8cfv 6123 . . 3 class (⊥‘(⊥‘ 𝑥))
112, 5, 10cmpt 4952 . 2 class (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
121, 11wceq 1658 1 wff = (𝑥 ∈ 𝒫 𝒫 ℋ ↦ (⊥‘(⊥‘ 𝑥)))
 Colors of variables: wff setvar class This definition is referenced by:  hsupval  28748
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