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Definition df-dgr 21618
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 21614 . 2  class deg
2 vf . . 3  setvar  f
3 cc 9276 . . . 4  class  CC
4 cply 21611 . . . 4  class Poly
53, 4cfv 5415 . . 3  class  (Poly `  CC )
62cv 1363 . . . . . . 7  class  f
7 ccoe 21613 . . . . . . 7  class coeff
86, 7cfv 5415 . . . . . 6  class  (coeff `  f )
98ccnv 4835 . . . . 5  class  `' (coeff `  f )
10 cc0 9278 . . . . . . 7  class  0
1110csn 3874 . . . . . 6  class  { 0 }
123, 11cdif 3322 . . . . 5  class  ( CC 
\  { 0 } )
139, 12cima 4839 . . . 4  class  ( `' (coeff `  f ) " ( CC  \  { 0 } ) )
14 cn0 10575 . . . 4  class  NN0
15 clt 9414 . . . 4  class  <
1613, 14, 15csup 7686 . . 3  class  sup (
( `' (coeff `  f ) " ( CC  \  { 0 } ) ) ,  NN0 ,  <  )
172, 5, 16cmpt 4347 . 2  class  ( f  e.  (Poly `  CC )  |->  sup ( ( `' (coeff `  f ) " ( CC  \  { 0 } ) ) ,  NN0 ,  <  ) )
181, 17wceq 1364 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  21655
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