HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  df-chsup Structured version   Unicode version

Definition df-chsup 25891
Description: Define the supremum of a set of Hilbert lattice elements. See chsupval2 25990 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 25919. (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 25513 . 2  class  \/H
2 vx . . 3  setvar  x
3 chil 25498 . . . . 5  class  ~H
43cpw 4003 . . . 4  class  ~P ~H
54cpw 4003 . . 3  class  ~P ~P ~H
62cv 1373 . . . . . 6  class  x
76cuni 4238 . . . . 5  class  U. x
8 cort 25509 . . . . 5  class  _|_
97, 8cfv 5579 . . . 4  class  ( _|_ `  U. x )
109, 8cfv 5579 . . 3  class  ( _|_ `  ( _|_ `  U. x ) )
112, 5, 10cmpt 4498 . 2  class  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
121, 11wceq 1374 1  wff  \/H  =  ( x  e.  ~P ~P ~H  |->  ( _|_ `  ( _|_ `  U. x ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  hsupval  25914
  Copyright terms: Public domain W3C validator