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Definition df-pellfund 30385
Description: A function mapping Pell discriminants to the corresponding fundamental solution. (Contributed by Stefan O'Rear, 18-Sep-2014.)
Assertion
Ref Expression
df-pellfund  |- PellFund  =  ( x  e.  ( NN 
\NN )  |->  sup ( { z  e.  (Pell14QR `  x
)  |  1  < 
z } ,  RR ,  `'  <  ) )
Distinct variable group:    x, z

Detailed syntax breakdown of Definition df-pellfund
StepHypRef Expression
1 cpellfund 30380 . 2  class PellFund
2 vx . . 3  setvar  x
3 cn 10532 . . . 4  class  NN
4 csquarenn 30376 . . . 4  classNN
53, 4cdif 3473 . . 3  class  ( NN 
\NN )
6 c1 9489 . . . . . 6  class  1
7 vz . . . . . . 7  setvar  z
87cv 1378 . . . . . 6  class  z
9 clt 9624 . . . . . 6  class  <
106, 8, 9wbr 4447 . . . . 5  wff  1  <  z
112cv 1378 . . . . . 6  class  x
12 cpell14qr 30379 . . . . . 6  class Pell14QR
1311, 12cfv 5586 . . . . 5  class  (Pell14QR `  x
)
1410, 7, 13crab 2818 . . . 4  class  { z  e.  (Pell14QR `  x
)  |  1  < 
z }
15 cr 9487 . . . 4  class  RR
169ccnv 4998 . . . 4  class  `'  <
1714, 15, 16csup 7896 . . 3  class  sup ( { z  e.  (Pell14QR `  x )  |  1  <  z } ,  RR ,  `'  <  )
182, 5, 17cmpt 4505 . 2  class  ( x  e.  ( NN  \NN )  |->  sup ( { z  e.  (Pell14QR `  x )  |  1  <  z } ,  RR ,  `'  <  ) )
191, 18wceq 1379 1  wff PellFund  =  ( x  e.  ( NN 
\NN )  |->  sup ( { z  e.  (Pell14QR `  x
)  |  1  < 
z } ,  RR ,  `'  <  ) )
Colors of variables: wff setvar class
This definition is referenced by:  pellfundval  30420
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