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Definition df-chsup 22815
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 22914 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 22843. (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 22439 . 2  class  \/H
2 vx . . 3  set  x
3 chil 22424 . . . . 5  class  ~H
43cpw 3801 . . . 4  class  ~P ~H
54cpw 3801 . . 3  class  ~P ~P ~H
62cv 1652 . . . . . 6  class  x
76cuni 4017 . . . . 5  class  U. x
8 cort 22435 . . . . 5  class  _|_
97, 8cfv 5456 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5456 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4268 . 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  22838
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