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Definition df-chsup 21720
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 21819 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 21748. (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 21344 . 2  class  \/H
2 vx . . 3  set  x
3 chil 21329 . . . . 5  class  ~H
43cpw 3530 . . . 4  class  ~P ~H
54cpw 3530 . . 3  class  ~P ~P ~H
62cv 1618 . . . . . 6  class  x
76cuni 3727 . . . . 5  class  U. x
8 cort 21340 . . . . 5  class  _|_
97, 8cfv 4592 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 4592 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 3974 . 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  21743
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