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Definition df-seqom 7031
Description: Index-aware recursive definitions over  om. A mashup of df-rdg 6994 and df-seq 12011, this allows for recursive definitions that use an index in the recursion in cases where Infinity is not admitted. (Contributed by Stefan O'Rear, 1-Nov-2014.)
Assertion
Ref Expression
df-seqom  |- seq𝜔 ( F ,  I
)  =  ( rec ( ( i  e. 
om ,  v  e. 
_V  |->  <. suc  i , 
( i F v ) >. ) ,  <. (/)
,  (  _I  `  I ) >. ) " om )
Distinct variable groups:    i, F, v    i, I, v

Detailed syntax breakdown of Definition df-seqom
StepHypRef Expression
1 cF . . 3  class  F
2 cI . . 3  class  I
31, 2cseqom 7030 . 2  class seq𝜔 ( F ,  I
)
4 vi . . . . 5  setvar  i
5 vv . . . . 5  setvar  v
6 com 6599 . . . . 5  class  om
7 cvv 3034 . . . . 5  class  _V
84cv 1398 . . . . . . 7  class  i
98csuc 4794 . . . . . 6  class  suc  i
105cv 1398 . . . . . . 7  class  v
118, 10, 1co 6196 . . . . . 6  class  ( i F v )
129, 11cop 3950 . . . . 5  class  <. suc  i ,  ( i F v ) >.
134, 5, 6, 7, 12cmpt2 6198 . . . 4  class  ( i  e.  om ,  v  e.  _V  |->  <. suc  i ,  ( i F v ) >. )
14 c0 3711 . . . . 5  class  (/)
15 cid 4704 . . . . . 6  class  _I
162, 15cfv 5496 . . . . 5  class  (  _I 
`  I )
1714, 16cop 3950 . . . 4  class  <. (/) ,  (  _I  `  I )
>.
1813, 17crdg 6993 . . 3  class  rec (
( i  e.  om ,  v  e.  _V  |->  <. suc  i ,  ( i F v )
>. ) ,  <. (/) ,  (  _I  `  I )
>. )
1918, 6cima 4916 . 2  class  ( rec ( ( i  e. 
om ,  v  e. 
_V  |->  <. suc  i , 
( i F v ) >. ) ,  <. (/)
,  (  _I  `  I ) >. ) " om )
203, 19wceq 1399 1  wff seq𝜔 ( F ,  I
)  =  ( rec ( ( i  e. 
om ,  v  e. 
_V  |->  <. suc  i , 
( i F v ) >. ) ,  <. (/)
,  (  _I  `  I ) >. ) " om )
Colors of variables: wff setvar class
This definition is referenced by:  seqomeq12  7037  fnseqom  7038  seqom0g  7039  seqomsuc  7040
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