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Definition df-watsN 29447
Description: Define W-atoms corresponding to an arbitrary "fiducial (i.e. reference) atom"  d. These are all atoms not in the polarity of  { d } ), which is the hyperplane determined by  d. Definition of set W in [Crawley] p. 111. (Contributed by NM, 26-Jan-2012.)
Assertion
Ref Expression
df-watsN  |-  WAtoms  =  ( k  e.  _V  |->  ( d  e.  ( Atoms `  k )  |->  ( (
Atoms `  k )  \ 
( ( _|_ P `  k ) `  {
d } ) ) ) )
Distinct variable group:    k, d

Detailed syntax breakdown of Definition df-watsN
StepHypRef Expression
1 cwpointsN 29443 . 2  class  WAtoms
2 vk . . 3  set  k
3 cvv 2790 . . 3  class  _V
4 vd . . . 4  set  d
52cv 1623 . . . . 5  class  k
6 catm 28721 . . . . 5  class  Atoms
75, 6cfv 5222 . . . 4  class  ( Atoms `  k )
84cv 1623 . . . . . . 7  class  d
98csn 3642 . . . . . 6  class  { d }
10 cpolN 29359 . . . . . . 7  class  _|_ P
115, 10cfv 5222 . . . . . 6  class  ( _|_
P `  k )
129, 11cfv 5222 . . . . 5  class  ( ( _|_ P `  k
) `  { d } )
137, 12cdif 3151 . . . 4  class  ( (
Atoms `  k )  \ 
( ( _|_ P `  k ) `  {
d } ) )
144, 7, 13cmpt 4079 . . 3  class  ( d  e.  ( Atoms `  k
)  |->  ( ( Atoms `  k )  \  (
( _|_ P `  k ) `  {
d } ) ) )
152, 3, 14cmpt 4079 . 2  class  ( k  e.  _V  |->  ( d  e.  ( Atoms `  k
)  |->  ( ( Atoms `  k )  \  (
( _|_ P `  k ) `  {
d } ) ) ) )
161, 15wceq 1624 1  wff  WAtoms  =  ( k  e.  _V  |->  ( d  e.  ( Atoms `  k )  |->  ( (
Atoms `  k )  \ 
( ( _|_ P `  k ) `  {
d } ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  watfvalN  29449
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