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Definition df-lsp 15745
Description: Define span of a set of vectors of a left module or left vector space. (Contributed by NM, 8-Dec-2013.)
Assertion
Ref Expression
df-lsp  |-  LSpan  =  ( w  e.  _V  |->  ( s  e.  ~P ( Base `  w )  |->  |^|
{ t  e.  (
LSubSp `  w )  |  s  C_  t }
) )
Distinct variable group:    w, s, t

Detailed syntax breakdown of Definition df-lsp
StepHypRef Expression
1 clspn 15744 . 2  class  LSpan
2 vw . . 3  set  w
3 cvv 2801 . . 3  class  _V
4 vs . . . 4  set  s
52cv 1631 . . . . . 6  class  w
6 cbs 13164 . . . . . 6  class  Base
75, 6cfv 5271 . . . . 5  class  ( Base `  w )
87cpw 3638 . . . 4  class  ~P ( Base `  w )
94cv 1631 . . . . . . 7  class  s
10 vt . . . . . . . 8  set  t
1110cv 1631 . . . . . . 7  class  t
129, 11wss 3165 . . . . . 6  wff  s  C_  t
13 clss 15705 . . . . . . 7  class  LSubSp
145, 13cfv 5271 . . . . . 6  class  ( LSubSp `  w )
1512, 10, 14crab 2560 . . . . 5  class  { t  e.  ( LSubSp `  w
)  |  s  C_  t }
1615cint 3878 . . . 4  class  |^| { t  e.  ( LSubSp `  w
)  |  s  C_  t }
174, 8, 16cmpt 4093 . . 3  class  ( s  e.  ~P ( Base `  w )  |->  |^| { t  e.  ( LSubSp `  w
)  |  s  C_  t } )
182, 3, 17cmpt 4093 . 2  class  ( w  e.  _V  |->  ( s  e.  ~P ( Base `  w )  |->  |^| { t  e.  ( LSubSp `  w
)  |  s  C_  t } ) )
191, 18wceq 1632 1  wff  LSpan  =  ( w  e.  _V  |->  ( s  e.  ~P ( Base `  w )  |->  |^|
{ t  e.  (
LSubSp `  w )  |  s  C_  t }
) )
Colors of variables: wff set class
This definition is referenced by:  lspfval  15746
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