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Definition df-chsup 21815
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 21914 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 21843. (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 21439 . 2  class  \/H
2 vx . . 3  set  x
3 chil 21424 . . . . 5  class  ~H
43cpw 3566 . . . 4  class  ~P ~H
54cpw 3566 . . 3  class  ~P ~P ~H
62cv 1618 . . . . . 6  class  x
76cuni 3768 . . . . 5  class  U. x
8 cort 21435 . . . . 5  class  _|_
97, 8cfv 4638 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 4638 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4017 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1619 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff set class
This definition is referenced by:  hsupval  21838
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