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Definition df-chsup 21836
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 21935 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 21864. (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 21460 . 2  class  \/H
2 vx . . 3  set  x
3 chil 21445 . . . . 5  class  ~H
43cpw 3585 . . . 4  class  ~P ~H
54cpw 3585 . . 3  class  ~P ~P ~H
62cv 1618 . . . . . 6  class  x
76cuni 3787 . . . . 5  class  U. x
8 cort 21456 . . . . 5  class  _|_
97, 8cfv 4659 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 4659 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4037 . 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  21859
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