Step | Hyp | Ref
| Expression |
1 | | eqid 2622 |
. . . . 5
Poly1 Poly1 |
2 | | eqid 2622 |
. . . . 5
var1 var1 |
3 | | eqid 2622 |
. . . . 5
.gmulGrpPoly1 .gmulGrpPoly1 |
4 | | crngring 18558 |
. . . . . . . 8
|
5 | | chcoeffeq.a |
. . . . . . . . 9
Mat |
6 | 5 | matring 20249 |
. . . . . . . 8
|
7 | 4, 6 | sylan2 491 |
. . . . . . 7
|
8 | 7 | 3adant3 1081 |
. . . . . 6
|
9 | 8 | adantr 481 |
. . . . 5
|
10 | | chcoeffeq.b |
. . . . 5
|
11 | | eqid 2622 |
. . . . 5
Poly1 Poly1 |
12 | | eqid 2622 |
. . . . 5
|
13 | | chcoeffeq.p |
. . . . . . . 8
Poly1 |
14 | | chcoeffeq.y |
. . . . . . . 8
Mat |
15 | | chcoeffeq.t |
. . . . . . . 8
matToPolyMat |
16 | | chcoeffeq.r |
. . . . . . . 8
|
17 | | chcoeffeq.s |
. . . . . . . 8
|
18 | | chcoeffeq.0 |
. . . . . . . 8
|
19 | | chcoeffeq.g |
. . . . . . . 8
|
20 | | eqid 2622 |
. . . . . . . 8
ConstPolyMat ConstPolyMat |
21 | | eqid 2622 |
. . . . . . . 8
|
22 | | eqid 2622 |
. . . . . . . 8
|
23 | | eqid 2622 |
. . . . . . . 8
var1 var1 |
24 | | eqid 2622 |
. . . . . . . 8
var1 var1 |
25 | | eqid 2622 |
. . . . . . . 8
maAdju maAdju |
26 | | chcoeffeq.w |
. . . . . . . 8
|
27 | | chcoeffeq.u |
. . . . . . . 8
cPolyMatToMat |
28 | 5, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 11, 3, 27 | cpmadumatpolylem1 20686 |
. . . . . . 7
|
29 | 28 | anasss 679 |
. . . . . 6
|
30 | 5, 10, 13, 14, 16, 17, 18, 15, 19, 20 | chfacfisfcpmat 20660 |
. . . . . . . . . . 11
ConstPolyMat |
31 | 4, 30 | syl3anl2 1375 |
. . . . . . . . . 10
ConstPolyMat |
32 | 31 | adantr 481 |
. . . . . . . . 9
ConstPolyMat |
33 | | fvco3 6275 |
. . . . . . . . . 10
ConstPolyMat |
34 | 33 | eqcomd 2628 |
. . . . . . . . 9
ConstPolyMat |
35 | 32, 34 | sylan 488 |
. . . . . . . 8
|
36 | | elmapi 7879 |
. . . . . . . . . 10
|
37 | 36 | adantl 482 |
. . . . . . . . 9
|
38 | 37 | ffvelrnda 6359 |
. . . . . . . 8
|
39 | 35, 38 | eqeltrd 2701 |
. . . . . . 7
|
40 | 39 | ralrimiva 2966 |
. . . . . 6
|
41 | 29, 40 | mpdan 702 |
. . . . 5
|
42 | 4 | anim2i 593 |
. . . . . . . . . 10
|
43 | 42 | 3adant3 1081 |
. . . . . . . . 9
|
44 | 43 | adantr 481 |
. . . . . . . 8
|
45 | 5, 10, 20, 27 | cpm2mf 20557 |
. . . . . . . 8
ConstPolyMat |
46 | 44, 45 | syl 17 |
. . . . . . 7
ConstPolyMat |
47 | | fcompt 6400 |
. . . . . . 7
ConstPolyMat ConstPolyMat
|
48 | 46, 31, 47 | syl2anc 693 |
. . . . . 6
|
49 | 5, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 11, 3, 27 | cpmadumatpolylem2 20687 |
. . . . . . 7
finSupp |
50 | 49 | anasss 679 |
. . . . . 6
finSupp |
51 | 48, 50 | eqbrtrrd 4677 |
. . . . 5
finSupp |
52 | | simpll1 1100 |
. . . . . . 7
|
53 | 4 | 3ad2ant2 1083 |
. . . . . . . 8
|
54 | 53 | ad2antrr 762 |
. . . . . . 7
|
55 | | chcoeffeq.k |
. . . . . . . . . 10
|
56 | | chcoeffeq.c |
. . . . . . . . . . 11
CharPlyMat
|
57 | | eqid 2622 |
. . . . . . . . . . 11
|
58 | 56, 5, 10, 13, 57 | chpmatply1 20637 |
. . . . . . . . . 10
|
59 | 55, 58 | syl5eqel 2705 |
. . . . . . . . 9
|
60 | | eqid 2622 |
. . . . . . . . . 10
coe1 coe1 |
61 | | eqid 2622 |
. . . . . . . . . 10
|
62 | 60, 57, 13, 61 | coe1fvalcl 19582 |
. . . . . . . . 9
coe1 |
63 | 59, 62 | sylan 488 |
. . . . . . . 8
coe1 |
64 | 63 | adantlr 751 |
. . . . . . 7
coe1 |
65 | | chcoeffeq.1 |
. . . . . . . . . 10
|
66 | 10, 65 | ringidcl 18568 |
. . . . . . . . 9
|
67 | 8, 66 | syl 17 |
. . . . . . . 8
|
68 | 67 | ad2antrr 762 |
. . . . . . 7
|
69 | | chcoeffeq.m |
. . . . . . . 8
|
70 | 61, 5, 10, 69 | matvscl 20237 |
. . . . . . 7
coe1
coe1 |
71 | 52, 54, 64, 68, 70 | syl22anc 1327 |
. . . . . 6
coe1
|
72 | 71 | ralrimiva 2966 |
. . . . 5
coe1 |
73 | | nn0ex 11298 |
. . . . . . 7
|
74 | 73 | a1i 11 |
. . . . . 6
|
75 | 5 | matlmod 20235 |
. . . . . . . . 9
|
76 | 4, 75 | sylan2 491 |
. . . . . . . 8
|
77 | 76 | 3adant3 1081 |
. . . . . . 7
|
78 | 77 | adantr 481 |
. . . . . 6
|
79 | | eqidd 2623 |
. . . . . 6
Scalar Scalar |
80 | | fvexd 6203 |
. . . . . 6
coe1 |
81 | | eqid 2622 |
. . . . . 6
Scalar Scalar |
82 | 5 | matsca2 20226 |
. . . . . . . . . 10
Scalar |
83 | 82 | 3adant3 1081 |
. . . . . . . . 9
Scalar |
84 | 83, 53 | eqeltrrd 2702 |
. . . . . . . 8
Scalar |
85 | 83 | eqcomd 2628 |
. . . . . . . . . . . 12
Scalar |
86 | 85 | fveq2d 6195 |
. . . . . . . . . . 11
Poly1Scalar Poly1 |
87 | 86, 13 | syl6eqr 2674 |
. . . . . . . . . 10
Poly1Scalar |
88 | 87 | fveq2d 6195 |
. . . . . . . . 9
Poly1Scalar |
89 | 59, 88 | eleqtrrd 2704 |
. . . . . . . 8
Poly1Scalar |
90 | | eqid 2622 |
. . . . . . . . 9
Poly1Scalar Poly1Scalar |
91 | | eqid 2622 |
. . . . . . . . 9
Poly1Scalar Poly1Scalar |
92 | 90, 91, 81 | mptcoe1fsupp 19585 |
. . . . . . . 8
Scalar
Poly1Scalar
coe1 finSupp Scalar |
93 | 84, 89, 92 | syl2anc 693 |
. . . . . . 7
coe1 finSupp
Scalar |
94 | 93 | adantr 481 |
. . . . . 6
coe1 finSupp Scalar |
95 | 74, 78, 79, 10, 80, 68, 12, 81, 69, 94 | mptscmfsupp0 18928 |
. . . . 5
coe1 finSupp |
96 | | fveq2 6191 |
. . . . . . . . . 10
|
97 | 96 | fveq2d 6195 |
. . . . . . . . 9
|
98 | | oveq1 6657 |
. . . . . . . . 9
.gmulGrpPoly1var1 .gmulGrpPoly1var1 |
99 | 97, 98 | oveq12d 6668 |
. . . . . . . 8
Poly1.gmulGrpPoly1var1 Poly1.gmulGrpPoly1var1 |
100 | 99 | cbvmptv 4750 |
. . . . . . 7
Poly1.gmulGrpPoly1var1 Poly1.gmulGrpPoly1var1 |
101 | 100 | oveq2i 6661 |
. . . . . 6
Poly1 g Poly1.gmulGrpPoly1var1 Poly1 g
Poly1.gmulGrpPoly1var1 |
102 | 101 | a1i 11 |
. . . . 5
Poly1 g Poly1.gmulGrpPoly1var1 Poly1 g
Poly1.gmulGrpPoly1var1 |
103 | | fveq2 6191 |
. . . . . . . . . 10
coe1 coe1 |
104 | 103 | oveq1d 6665 |
. . . . . . . . 9
coe1
coe1 |
105 | 104, 98 | oveq12d 6668 |
. . . . . . . 8
coe1 Poly1.gmulGrpPoly1var1 coe1 Poly1.gmulGrpPoly1var1 |
106 | 105 | cbvmptv 4750 |
. . . . . . 7
coe1 Poly1.gmulGrpPoly1var1 coe1 Poly1.gmulGrpPoly1var1 |
107 | 106 | oveq2i 6661 |
. . . . . 6
Poly1 g coe1 Poly1.gmulGrpPoly1var1 Poly1 g
coe1 Poly1.gmulGrpPoly1var1 |
108 | 107 | a1i 11 |
. . . . 5
Poly1 g coe1 Poly1.gmulGrpPoly1var1 Poly1 g
coe1 Poly1.gmulGrpPoly1var1 |
109 | 1, 2, 3, 9, 10, 11, 12, 41, 51, 72, 95, 102, 108 | gsumply1eq 19675 |
. . . 4
Poly1 g Poly1.gmulGrpPoly1var1 Poly1 g
coe1 Poly1.gmulGrpPoly1var1
coe1 |
110 | 109 | biimpa 501 |
. . 3
Poly1 g
Poly1.gmulGrpPoly1var1 Poly1 g
coe1 Poly1.gmulGrpPoly1var1 coe1 |
111 | 97, 104 | eqeq12d 2637 |
. . . 4
coe1 coe1 |
112 | 111 | cbvralv 3171 |
. . 3
coe1
coe1 |
113 | 110, 112 | sylibr 224 |
. 2
Poly1 g
Poly1.gmulGrpPoly1var1 Poly1 g
coe1 Poly1.gmulGrpPoly1var1 coe1 |
114 | 113 | ex 450 |
1
Poly1 g Poly1.gmulGrpPoly1var1 Poly1 g
coe1 Poly1.gmulGrpPoly1var1
coe1 |