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Definition df-chsup 21882
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 21981 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 21910. (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 21506 . 2  class  \/H
2 vx . . 3  set  x
3 chil 21491 . . . . 5  class  ~H
43cpw 3626 . . . 4  class  ~P ~H
54cpw 3626 . . 3  class  ~P ~P ~H
62cv 1627 . . . . . 6  class  x
76cuni 3828 . . . . 5  class  U. x
8 cort 21502 . . . . 5  class  _|_
97, 8cfv 5221 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5221 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4078 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1628 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff set class
This definition is referenced by:  hsupval  21905
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