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Definition df-chsup 21906
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 22005 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 21934. (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 21530 . 2  class  \/H
2 vx . . 3  set  x
3 chil 21515 . . . . 5  class  ~H
43cpw 3638 . . . 4  class  ~P ~H
54cpw 3638 . . 3  class  ~P ~P ~H
62cv 1631 . . . . . 6  class  x
76cuni 3843 . . . . 5  class  U. x
8 cort 21526 . . . . 5  class  _|_
97, 8cfv 5271 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5271 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4093 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1632 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff set class
This definition is referenced by:  hsupval  21929
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