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Definition df-chsup 24717
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 24816 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 24745. (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 24339 . 2  class  \/H
2 vx . . 3  setvar  x
3 chil 24324 . . . . 5  class  ~H
43cpw 3863 . . . 4  class  ~P ~H
54cpw 3863 . . 3  class  ~P ~P ~H
62cv 1368 . . . . . 6  class  x
76cuni 4094 . . . . 5  class  U. x
8 cort 24335 . . . . 5  class  _|_
97, 8cfv 5421 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5421 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4353 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1369 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  24740
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