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Definition df-chsup 22814
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 22913 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 22842. (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 22438 . 2  class  \/H
2 vx . . 3  set  x
3 chil 22423 . . . . 5  class  ~H
43cpw 3800 . . . 4  class  ~P ~H
54cpw 3800 . . 3  class  ~P ~P ~H
62cv 1652 . . . . . 6  class  x
76cuni 4016 . . . . 5  class  U. x
8 cort 22434 . . . . 5  class  _|_
97, 8cfv 5455 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5455 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4267 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1653 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff set class
This definition is referenced by:  hsupval  22837
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