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Definition df-pws 13675
Description: Define a structure power, which is just a structure product where all the factors are the same. (Contributed by Mario Carneiro, 11-Jan-2015.)
Assertion
Ref Expression
df-pws  |-  ^s  =  ( r  e.  _V , 
i  e.  _V  |->  ( (Scalar `  r ) X_s ( i  X.  { r } ) ) )
Distinct variable group:    i, r

Detailed syntax breakdown of Definition df-pws
StepHypRef Expression
1 cpws 13672 . 2  class  ^s
2 vr . . 3  set  r
3 vi . . 3  set  i
4 cvv 2958 . . 3  class  _V
52cv 1652 . . . . 5  class  r
6 csca 13534 . . . . 5  class Scalar
75, 6cfv 5456 . . . 4  class  (Scalar `  r )
83cv 1652 . . . . 5  class  i
95csn 3816 . . . . 5  class  { r }
108, 9cxp 4878 . . . 4  class  ( i  X.  { r } )
11 cprds 13671 . . . 4  class  X_s
127, 10, 11co 6083 . . 3  class  ( (Scalar `  r ) X_s ( i  X.  {
r } ) )
132, 3, 4, 4, 12cmpt2 6085 . 2  class  ( r  e.  _V ,  i  e.  _V  |->  ( (Scalar `  r ) X_s ( i  X.  {
r } ) ) )
141, 13wceq 1653 1  wff  ^s  =  ( r  e.  _V , 
i  e.  _V  |->  ( (Scalar `  r ) X_s ( i  X.  { r } ) ) )
Colors of variables: wff set class
This definition is referenced by:  pwsval  13710
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