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Definition df-chsup 22766
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 22865 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 22794. (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 22390 . 2  class  \/H
2 vx . . 3  set  x
3 chil 22375 . . . . 5  class  ~H
43cpw 3759 . . . 4  class  ~P ~H
54cpw 3759 . . 3  class  ~P ~P ~H
62cv 1648 . . . . . 6  class  x
76cuni 3975 . . . . 5  class  U. x
8 cort 22386 . . . . 5  class  _|_
97, 8cfv 5413 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5413 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4226 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1649 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff set class
This definition is referenced by:  hsupval  22789
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