ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-shft Unicode version

Definition df-shft 10542
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 10552 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 10541 . 2  class  shift
2 vf . . 3  setvar  f
3 vx . . 3  setvar  x
4 cvv 2660 . . 3  class  _V
5 cc 7586 . . 3  class  CC
6 vy . . . . . . 7  setvar  y
76cv 1315 . . . . . 6  class  y
87, 5wcel 1465 . . . . 5  wff  y  e.  CC
93cv 1315 . . . . . . 7  class  x
10 cmin 7901 . . . . . . 7  class  -
117, 9, 10co 5742 . . . . . 6  class  ( y  -  x )
12 vz . . . . . . 7  setvar  z
1312cv 1315 . . . . . 6  class  z
142cv 1315 . . . . . 6  class  f
1511, 13, 14wbr 3899 . . . . 5  wff  ( y  -  x ) f z
168, 15wa 103 . . . 4  wff  ( y  e.  CC  /\  (
y  -  x ) f z )
1716, 6, 12copab 3958 . . 3  class  { <. y ,  z >.  |  ( y  e.  CC  /\  ( y  -  x
) f z ) }
182, 3, 4, 5, 17cmpo 5744 . 2  class  ( f  e.  _V ,  x  e.  CC  |->  { <. y ,  z >.  |  ( y  e.  CC  /\  ( y  -  x
) f z ) } )
191, 18wceq 1316 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:  shftfvalg  10545  shftfval  10548
  Copyright terms: Public domain W3C validator