| Step |
Hyp |
Ref |
Expression |
| 1 |
|
elrgspn.b |
|
| 2 |
|
elrgspn.m |
|
| 3 |
|
elrgspn.x |
|
| 4 |
|
elrgspn.n |
|
| 5 |
|
elrgspn.f |
|
| 6 |
|
elrgspn.r |
|
| 7 |
|
elrgspn.a |
|
| 8 |
|
elrgspnlem1.1 |
|
| 9 |
|
eqid |
|
| 10 |
|
fveq1 |
|
| 11 |
10
|
oveq1d |
|
| 12 |
11
|
mpteq2dv |
|
| 13 |
12
|
oveq2d |
|
| 14 |
13
|
eqeq2d |
|
| 15 |
|
breq1 |
|
| 16 |
|
zex |
|
| 17 |
16
|
a1i |
|
| 18 |
1
|
fvexi |
|
| 19 |
18
|
a1i |
|
| 20 |
19 7
|
ssexd |
|
| 21 |
|
wrdexg |
|
| 22 |
20 21
|
syl |
|
| 23 |
22
|
adantr |
|
| 24 |
|
1zzd |
|
| 25 |
|
0zd |
|
| 26 |
24 25
|
ifclda |
|
| 27 |
26
|
fmpttd |
|
| 28 |
17 23 27
|
elmapdd |
|
| 29 |
28
|
elexd |
|
| 30 |
27
|
ffund |
|
| 31 |
|
0zd |
|
| 32 |
|
snfi |
|
| 33 |
32
|
a1i |
|
| 34 |
|
eldifsni |
|
| 35 |
34
|
adantl |
|
| 36 |
35
|
neneqd |
|
| 37 |
36
|
iffalsed |
|
| 38 |
37 23
|
suppss2 |
|
| 39 |
|
suppssfifsupp |
|
| 40 |
29 30 31 33 38 39
|
syl32anc |
|
| 41 |
15 28 40
|
elrabd |
|
| 42 |
41 5
|
eleqtrrdi |
|
| 43 |
|
eqeq2 |
|
| 44 |
|
eqeq2 |
|
| 45 |
|
eqid |
|
| 46 |
|
simpr |
|
| 47 |
|
simplr |
|
| 48 |
46 47
|
eqtrd |
|
| 49 |
48
|
iftrued |
|
| 50 |
|
simplr |
|
| 51 |
|
1zzd |
|
| 52 |
45 49 50 51
|
fvmptd2 |
|
| 53 |
|
simpr |
|
| 54 |
53
|
oveq2d |
|
| 55 |
7
|
sselda |
|
| 56 |
55
|
ad2antrr |
|
| 57 |
2 1
|
mgpbas |
|
| 58 |
57
|
gsumws1 |
|
| 59 |
56 58
|
syl |
|
| 60 |
54 59
|
eqtrd |
|
| 61 |
52 60
|
oveq12d |
|
| 62 |
1 3
|
mulg1 |
|
| 63 |
56 62
|
syl |
|
| 64 |
61 63
|
eqtrd |
|
| 65 |
|
eqeq1 |
|
| 66 |
65
|
notbid |
|
| 67 |
66
|
biimparc |
|
| 68 |
67
|
adantll |
|
| 69 |
68
|
iffalsed |
|
| 70 |
|
simplr |
|
| 71 |
|
0zd |
|
| 72 |
45 69 70 71
|
fvmptd2 |
|
| 73 |
72
|
oveq1d |
|
| 74 |
2
|
ringmgp |
|
| 75 |
6 74
|
syl |
|
| 76 |
75
|
ad3antrrr |
|
| 77 |
|
sswrd |
|
| 78 |
7 77
|
syl |
|
| 79 |
78
|
adantr |
|
| 80 |
79
|
sselda |
|
| 81 |
80
|
adantr |
|
| 82 |
57
|
gsumwcl |
|
| 83 |
76 81 82
|
syl2anc |
|
| 84 |
|
eqid |
|
| 85 |
1 84 3
|
mulg0 |
|
| 86 |
83 85
|
syl |
|
| 87 |
73 86
|
eqtrd |
|
| 88 |
43 44 64 87
|
ifbothda |
|
| 89 |
88
|
mpteq2dva |
|
| 90 |
89
|
oveq2d |
|
| 91 |
|
ringmnd |
|
| 92 |
6 91
|
syl |
|
| 93 |
92
|
adantr |
|
| 94 |
|
simpr |
|
| 95 |
94
|
s1cld |
|
| 96 |
|
eqid |
|
| 97 |
7 1
|
sseqtrdi |
|
| 98 |
97
|
sselda |
|
| 99 |
84 93 23 95 96 98
|
gsummptif1n0 |
|
| 100 |
90 99
|
eqtr2d |
|
| 101 |
14 42 100
|
rspcedvdw |
|
| 102 |
9 101 94
|
elrnmptd |
|
| 103 |
102 8
|
eleqtrrdi |
|
| 104 |
103
|
ex |
|
| 105 |
104
|
ssrdv |
|