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Definition df-chsup 24537
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 24636 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 24565. (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 24159 . 2  class  \/H
2 vx . . 3  setvar  x
3 chil 24144 . . . . 5  class  ~H
43cpw 3848 . . . 4  class  ~P ~H
54cpw 3848 . . 3  class  ~P ~P ~H
62cv 1361 . . . . . 6  class  x
76cuni 4079 . . . . 5  class  U. x
8 cort 24155 . . . . 5  class  _|_
97, 8cfv 5406 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5406 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4338 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1362 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  24560
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