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Definition df-chsup 21890
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 21989 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 21918. (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 21514 . 2  class  \/H
2 vx . . 3  set  x
3 chil 21499 . . . . 5  class  ~H
43cpw 3625 . . . 4  class  ~P ~H
54cpw 3625 . . 3  class  ~P ~P ~H
62cv 1622 . . . . . 6  class  x
76cuni 3827 . . . . 5  class  U. x
8 cort 21510 . . . . 5  class  _|_
97, 8cfv 5255 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5255 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4077 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1623 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff set class
This definition is referenced by:  hsupval  21913
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