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Definition df-shft 11562
Description: Define a function shifter. This operation offsets the value argument of a function (ordinarily on a subset of  CC) and produces a new function on  CC. See shftval 11569 for its value. (Contributed by NM, 20-Jul-2005.)
Assertion
Ref Expression
df-shft  |-  shift  =  ( f  e.  _V ,  x  e.  CC  |->  { <. y ,  z >.  |  ( y  e.  CC  /\  ( y  -  x
) f z ) } )
Distinct variable group:    x, y, z, f

Detailed syntax breakdown of Definition df-shft
StepHypRef Expression
1 cshi 11561 . 2  class  shift
2 vf . . 3  set  f
3 vx . . 3  set  x
4 cvv 2788 . . 3  class  _V
5 cc 8735 . . 3  class  CC
6 vy . . . . . . 7  set  y
76cv 1622 . . . . . 6  class  y
87, 5wcel 1684 . . . . 5  wff  y  e.  CC
93cv 1622 . . . . . . 7  class  x
10 cmin 9037 . . . . . . 7  class  -
117, 9, 10co 5858 . . . . . 6  class  ( y  -  x )
12 vz . . . . . . 7  set  z
1312cv 1622 . . . . . 6  class  z
142cv 1622 . . . . . 6  class  f
1511, 13, 14wbr 4023 . . . . 5  wff  ( y  -  x ) f z
168, 15wa 358 . . . 4  wff  ( y  e.  CC  /\  (
y  -  x ) f z )
1716, 6, 12copab 4076 . . 3  class  { <. y ,  z >.  |  ( y  e.  CC  /\  ( y  -  x
) f z ) }
182, 3, 4, 5, 17cmpt2 5860 . 2  class  ( f  e.  _V ,  x  e.  CC  |->  { <. y ,  z >.  |  ( y  e.  CC  /\  ( y  -  x
) f z ) } )
191, 18wceq 1623 1  wff  shift  =  ( f  e.  _V ,  x  e.  CC  |->  { <. y ,  z >.  |  ( y  e.  CC  /\  ( y  -  x
) f z ) } )
Colors of variables: wff set class
This definition is referenced by:  shftfval  11565
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