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Definition df-chsup 26643
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 26742 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 26671. (Contributed by NM, 9-Dec-2003.) (New usage is discouraged.)
Assertion
Ref Expression
df-chsup  |-  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )

Detailed syntax breakdown of Definition df-chsup
StepHypRef Expression
1 chsup 26265 . 2  class  \/H
2 vx . . 3  setvar  x
3 chil 26250 . . . . 5  class  ~H
43cpw 3955 . . . 4  class  ~P ~H
54cpw 3955 . . 3  class  ~P ~P ~H
62cv 1404 . . . . . 6  class  x
76cuni 4191 . . . . 5  class  U. x
8 cort 26261 . . . . 5  class  _|_
97, 8cfv 5569 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5569 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4453 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1405 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  26666
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