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

Definition df-span 22811
Description: Define the linear span of a subset of Hilbert space. Definition of span in [Schechter] p. 276. See spanval 22835 for its value. (Contributed by NM, 2-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
df-span  |-  span  =  ( x  e.  ~P ~H  |->  |^| { y  e.  SH  |  x  C_  y } )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-span
StepHypRef Expression
1 cspn 22435 . 2  class  span
2 vx . . 3  set  x
3 chil 22422 . . . 4  class  ~H
43cpw 3799 . . 3  class  ~P ~H
52cv 1651 . . . . . 6  class  x
6 vy . . . . . . 7  set  y
76cv 1651 . . . . . 6  class  y
85, 7wss 3320 . . . . 5  wff  x  C_  y
9 csh 22431 . . . . 5  class  SH
108, 6, 9crab 2709 . . . 4  class  { y  e.  SH  |  x 
C_  y }
1110cint 4050 . . 3  class  |^| { y  e.  SH  |  x 
C_  y }
122, 4, 11cmpt 4266 . 2  class  ( x  e.  ~P ~H  |->  |^|
{ y  e.  SH  |  x  C_  y } )
131, 12wceq 1652 1  wff  span  =  ( x  e.  ~P ~H  |->  |^| { y  e.  SH  |  x  C_  y } )
Colors of variables: wff set class
This definition is referenced by:  spanval  22835
  Copyright terms: Public domain W3C validator