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

Definition df-chj 22765
Description: Define Hilbert lattice join. See chjval 22807 for its value and chjcl 22812 for its closure law. Note that we define it over all Hilbert space subsets to allow proving more general theorems. Even for general subsets the join belongs to  CH; see sshjcl 22810. (Contributed by NM, 1-Nov-2000.) (New usage is discouraged.)
Assertion
Ref Expression
df-chj  |-  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-chj
StepHypRef Expression
1 chj 22389 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 22375 . . . 4  class  ~H
54cpw 3759 . . 3  class  ~P ~H
62cv 1648 . . . . . 6  class  x
73cv 1648 . . . . . 6  class  y
86, 7cun 3278 . . . . 5  class  ( x  u.  y )
9 cort 22386 . . . . 5  class  _|_
108, 9cfv 5413 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5413 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6042 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1649 1  wff  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  sshjval  22805
  Copyright terms: Public domain W3C validator