Step |
Hyp |
Ref |
Expression |
1 |
|
lgseisen.1 |
|
2 |
|
lgseisen.2 |
|
3 |
|
lgseisen.3 |
|
4 |
|
lgsquad.4 |
|
5 |
|
lgsquad.5 |
|
6 |
|
lgsquad.6 |
|
7 |
3
|
necomd |
|
8 |
|
eleq1w |
|
9 |
|
eleq1w |
|
10 |
8 9
|
bi2anan9 |
|
11 |
10
|
biancomd |
|
12 |
|
oveq1 |
|
13 |
|
oveq1 |
|
14 |
12 13
|
breqan12d |
|
15 |
11 14
|
anbi12d |
|
16 |
15
|
ancoms |
|
17 |
16
|
cbvopabv |
|
18 |
2 1 7 5 4 17
|
lgsquadlem2 |
|
19 |
|
relopab |
|
20 |
|
fzfid |
|
21 |
|
fzfid |
|
22 |
|
xpfi |
|
23 |
20 21 22
|
syl2anc |
|
24 |
|
opabssxp |
|
25 |
|
ssfi |
|
26 |
23 24 25
|
sylancl |
|
27 |
|
cnven |
|
28 |
19 26 27
|
sylancr |
|
29 |
|
cnvopab |
|
30 |
28 29
|
breqtrdi |
|
31 |
|
hasheni |
|
32 |
30 31
|
syl |
|
33 |
32
|
oveq2d |
|
34 |
18 33
|
eqtr4d |
|
35 |
1 2 3 4 5 6
|
lgsquadlem2 |
|
36 |
34 35
|
oveq12d |
|
37 |
|
neg1cn |
|
38 |
37
|
a1i |
|
39 |
|
opabssxp |
|
40 |
6 39
|
eqsstri |
|
41 |
|
ssfi |
|
42 |
23 40 41
|
sylancl |
|
43 |
|
hashcl |
|
44 |
42 43
|
syl |
|
45 |
|
hashcl |
|
46 |
26 45
|
syl |
|
47 |
38 44 46
|
expaddd |
|
48 |
2
|
eldifad |
|
49 |
48
|
adantr |
|
50 |
|
prmnn |
|
51 |
49 50
|
syl |
|
52 |
2 5
|
gausslemma2dlem0b |
|
53 |
52
|
adantr |
|
54 |
53
|
nnzd |
|
55 |
|
prmz |
|
56 |
49 55
|
syl |
|
57 |
|
peano2zm |
|
58 |
56 57
|
syl |
|
59 |
53
|
nnred |
|
60 |
58
|
zred |
|
61 |
|
prmuz2 |
|
62 |
49 61
|
syl |
|
63 |
|
uz2m1nn |
|
64 |
62 63
|
syl |
|
65 |
64
|
nnrpd |
|
66 |
|
rphalflt |
|
67 |
65 66
|
syl |
|
68 |
5 67
|
eqbrtrid |
|
69 |
59 60 68
|
ltled |
|
70 |
|
eluz2 |
|
71 |
54 58 69 70
|
syl3anbrc |
|
72 |
|
fzss2 |
|
73 |
71 72
|
syl |
|
74 |
|
simprr |
|
75 |
73 74
|
sseldd |
|
76 |
|
fzm1ndvds |
|
77 |
51 75 76
|
syl2anc |
|
78 |
7
|
adantr |
|
79 |
1
|
eldifad |
|
80 |
79
|
adantr |
|
81 |
|
prmrp |
|
82 |
49 80 81
|
syl2anc |
|
83 |
78 82
|
mpbird |
|
84 |
|
prmz |
|
85 |
80 84
|
syl |
|
86 |
|
elfzelz |
|
87 |
86
|
ad2antll |
|
88 |
|
coprmdvds |
|
89 |
56 85 87 88
|
syl3anc |
|
90 |
83 89
|
mpan2d |
|
91 |
77 90
|
mtod |
|
92 |
|
prmnn |
|
93 |
80 92
|
syl |
|
94 |
93
|
nncnd |
|
95 |
|
elfznn |
|
96 |
95
|
ad2antll |
|
97 |
96
|
nncnd |
|
98 |
94 97
|
mulcomd |
|
99 |
98
|
breq2d |
|
100 |
91 99
|
mtbid |
|
101 |
|
elfzelz |
|
102 |
101
|
ad2antrl |
|
103 |
|
dvdsmul2 |
|
104 |
102 56 103
|
syl2anc |
|
105 |
|
breq2 |
|
106 |
104 105
|
syl5ibcom |
|
107 |
106
|
necon3bd |
|
108 |
100 107
|
mpd |
|
109 |
|
elfznn |
|
110 |
109
|
ad2antrl |
|
111 |
110 51
|
nnmulcld |
|
112 |
111
|
nnred |
|
113 |
96 93
|
nnmulcld |
|
114 |
113
|
nnred |
|
115 |
112 114
|
lttri2d |
|
116 |
108 115
|
mpbid |
|
117 |
116
|
ex |
|
118 |
117
|
pm4.71rd |
|
119 |
|
ancom |
|
120 |
118 119
|
bitr2di |
|
121 |
120
|
opabbidv |
|
122 |
|
unopab |
|
123 |
6
|
uneq2i |
|
124 |
|
andi |
|
125 |
124
|
opabbii |
|
126 |
122 123 125
|
3eqtr4i |
|
127 |
|
df-xp |
|
128 |
121 126 127
|
3eqtr4g |
|
129 |
128
|
fveq2d |
|
130 |
|
inopab |
|
131 |
6
|
ineq2i |
|
132 |
|
anandi |
|
133 |
132
|
opabbii |
|
134 |
130 131 133
|
3eqtr4i |
|
135 |
|
ltnsym2 |
|
136 |
112 114 135
|
syl2anc |
|
137 |
136
|
ex |
|
138 |
|
imnan |
|
139 |
137 138
|
sylib |
|
140 |
139
|
nexdv |
|
141 |
140
|
nexdv |
|
142 |
|
opabn0 |
|
143 |
142
|
necon1bbii |
|
144 |
141 143
|
sylib |
|
145 |
134 144
|
syl5eq |
|
146 |
|
hashun |
|
147 |
26 42 145 146
|
syl3anc |
|
148 |
|
hashxp |
|
149 |
20 21 148
|
syl2anc |
|
150 |
1 4
|
gausslemma2dlem0b |
|
151 |
150
|
nnnn0d |
|
152 |
|
hashfz1 |
|
153 |
151 152
|
syl |
|
154 |
52
|
nnnn0d |
|
155 |
|
hashfz1 |
|
156 |
154 155
|
syl |
|
157 |
153 156
|
oveq12d |
|
158 |
149 157
|
eqtrd |
|
159 |
129 147 158
|
3eqtr3d |
|
160 |
159
|
oveq2d |
|
161 |
36 47 160
|
3eqtr2d |
|