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Definition df-dgr 22316
Description: Define the degree of a polynomial. (Contributed by Mario Carneiro, 22-Jul-2014.)
Assertion
Ref Expression
df-dgr  |- deg  =  ( f  e.  (Poly `  CC )  |->  sup (
( `' (coeff `  f ) " ( CC  \  { 0 } ) ) ,  NN0 ,  <  ) )

Detailed syntax breakdown of Definition df-dgr
StepHypRef Expression
1 cdgr 22312 . 2  class deg
2 vf . . 3  setvar  f
3 cc 9479 . . . 4  class  CC
4 cply 22309 . . . 4  class Poly
53, 4cfv 5579 . . 3  class  (Poly `  CC )
62cv 1373 . . . . . . 7  class  f
7 ccoe 22311 . . . . . . 7  class coeff
86, 7cfv 5579 . . . . . 6  class  (coeff `  f )
98ccnv 4991 . . . . 5  class  `' (coeff `  f )
10 cc0 9481 . . . . . . 7  class  0
1110csn 4020 . . . . . 6  class  { 0 }
123, 11cdif 3466 . . . . 5  class  ( CC 
\  { 0 } )
139, 12cima 4995 . . . 4  class  ( `' (coeff `  f ) " ( CC  \  { 0 } ) )
14 cn0 10784 . . . 4  class  NN0
15 clt 9617 . . . 4  class  <
1613, 14, 15csup 7889 . . 3  class  sup (
( `' (coeff `  f ) " ( CC  \  { 0 } ) ) ,  NN0 ,  <  )
172, 5, 16cmpt 4498 . 2  class  ( f  e.  (Poly `  CC )  |->  sup ( ( `' (coeff `  f ) " ( CC  \  { 0 } ) ) ,  NN0 ,  <  ) )
181, 17wceq 1374 1  wff deg  =  ( f  e.  (Poly `  CC )  |->  sup (
( `' (coeff `  f ) " ( CC  \  { 0 } ) ) ,  NN0 ,  <  ) )
Colors of variables: wff setvar class
This definition is referenced by:  dgrval  22353
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