Step | Hyp | Ref
| Expression |
1 | | cquot 26027 |
. 2
class
quot |
2 | | vf |
. . 3
setvar π |
3 | | vg |
. . 3
setvar π |
4 | | cc 11110 |
. . . 4
class
β |
5 | | cply 25922 |
. . . 4
class
Poly |
6 | 4, 5 | cfv 6543 |
. . 3
class
(Polyββ) |
7 | | c0p 25410 |
. . . . 5
class
0π |
8 | 7 | csn 4628 |
. . . 4
class
{0π} |
9 | 6, 8 | cdif 3945 |
. . 3
class
((Polyββ) β {0π}) |
10 | | vr |
. . . . . . . 8
setvar π |
11 | 10 | cv 1540 |
. . . . . . 7
class π |
12 | 11, 7 | wceq 1541 |
. . . . . 6
wff π =
0π |
13 | | cdgr 25925 |
. . . . . . . 8
class
deg |
14 | 11, 13 | cfv 6543 |
. . . . . . 7
class
(degβπ) |
15 | 3 | cv 1540 |
. . . . . . . 8
class π |
16 | 15, 13 | cfv 6543 |
. . . . . . 7
class
(degβπ) |
17 | | clt 11252 |
. . . . . . 7
class
< |
18 | 14, 16, 17 | wbr 5148 |
. . . . . 6
wff
(degβπ) <
(degβπ) |
19 | 12, 18 | wo 845 |
. . . . 5
wff (π = 0π β¨
(degβπ) <
(degβπ)) |
20 | 2 | cv 1540 |
. . . . . 6
class π |
21 | | vq |
. . . . . . . 8
setvar π |
22 | 21 | cv 1540 |
. . . . . . 7
class π |
23 | | cmul 11117 |
. . . . . . . 8
class
Β· |
24 | 23 | cof 7670 |
. . . . . . 7
class
βf Β· |
25 | 15, 22, 24 | co 7411 |
. . . . . 6
class (π βf Β·
π) |
26 | | cmin 11448 |
. . . . . . 7
class
β |
27 | 26 | cof 7670 |
. . . . . 6
class
βf β |
28 | 20, 25, 27 | co 7411 |
. . . . 5
class (π βf β
(π βf
Β· π)) |
29 | 19, 10, 28 | wsbc 3777 |
. . . 4
wff
[(π
βf β (π βf Β· π)) / π](π = 0π β¨
(degβπ) <
(degβπ)) |
30 | 29, 21, 6 | crio 7366 |
. . 3
class
(β©π
β (Polyββ)[(π βf β (π βf Β·
π)) / π](π = 0π β¨
(degβπ) <
(degβπ))) |
31 | 2, 3, 6, 9, 30 | cmpo 7413 |
. 2
class (π β (Polyββ),
π β
((Polyββ) β {0π}) β¦
(β©π β
(Polyββ)[(π βf β (π βf Β·
π)) / π](π = 0π β¨
(degβπ) <
(degβπ)))) |
32 | 1, 31 | wceq 1541 |
1
wff quot =
(π β
(Polyββ), π
β ((Polyββ) β {0π}) β¦
(β©π β
(Polyββ)[(π βf β (π βf Β·
π)) / π](π = 0π β¨
(degβπ) <
(degβπ)))) |