Step |
Hyp |
Ref |
Expression |
1 |
|
3nn0 |
|
2 |
|
bpolyval |
|
3 |
1 2
|
mpan |
|
4 |
|
3m1e2 |
|
5 |
|
df-2 |
|
6 |
4 5
|
eqtri |
|
7 |
6
|
oveq2i |
|
8 |
7
|
sumeq1i |
|
9 |
|
1eluzge0 |
|
10 |
9
|
a1i |
|
11 |
|
0z |
|
12 |
|
fzpr |
|
13 |
11 12
|
ax-mp |
|
14 |
|
0p1e1 |
|
15 |
14
|
oveq2i |
|
16 |
14
|
preq2i |
|
17 |
13 15 16
|
3eqtr3ri |
|
18 |
5
|
sneqi |
|
19 |
17 18
|
uneq12i |
|
20 |
|
df-tp |
|
21 |
|
fzsuc |
|
22 |
9 21
|
ax-mp |
|
23 |
19 20 22
|
3eqtr4ri |
|
24 |
23
|
eleq2i |
|
25 |
|
vex |
|
26 |
25
|
eltp |
|
27 |
24 26
|
bitri |
|
28 |
|
oveq2 |
|
29 |
|
bcn0 |
|
30 |
1 29
|
ax-mp |
|
31 |
28 30
|
eqtrdi |
|
32 |
|
oveq1 |
|
33 |
|
oveq2 |
|
34 |
33
|
oveq1d |
|
35 |
|
3cn |
|
36 |
35
|
subid1i |
|
37 |
36
|
oveq1i |
|
38 |
|
df-4 |
|
39 |
37 38
|
eqtr4i |
|
40 |
34 39
|
eqtrdi |
|
41 |
32 40
|
oveq12d |
|
42 |
31 41
|
oveq12d |
|
43 |
|
bpoly0 |
|
44 |
43
|
oveq1d |
|
45 |
44
|
oveq2d |
|
46 |
|
4cn |
|
47 |
|
4ne0 |
|
48 |
46 47
|
reccli |
|
49 |
48
|
mulid2i |
|
50 |
45 49
|
eqtrdi |
|
51 |
42 50
|
sylan9eqr |
|
52 |
51 48
|
eqeltrdi |
|
53 |
|
oveq2 |
|
54 |
|
bcn1 |
|
55 |
1 54
|
ax-mp |
|
56 |
53 55
|
eqtrdi |
|
57 |
|
oveq1 |
|
58 |
|
oveq2 |
|
59 |
58
|
oveq1d |
|
60 |
|
ax-1cn |
|
61 |
|
npcan |
|
62 |
35 60 61
|
mp2an |
|
63 |
59 62
|
eqtrdi |
|
64 |
57 63
|
oveq12d |
|
65 |
56 64
|
oveq12d |
|
66 |
|
bpoly1 |
|
67 |
66
|
oveq1d |
|
68 |
67
|
oveq2d |
|
69 |
|
halfcn |
|
70 |
|
subcl |
|
71 |
69 70
|
mpan2 |
|
72 |
|
3ne0 |
|
73 |
|
divcan2 |
|
74 |
35 72 73
|
mp3an23 |
|
75 |
71 74
|
syl |
|
76 |
68 75
|
eqtrd |
|
77 |
65 76
|
sylan9eqr |
|
78 |
71
|
adantr |
|
79 |
77 78
|
eqeltrd |
|
80 |
|
oveq2 |
|
81 |
|
bcn2 |
|
82 |
1 81
|
ax-mp |
|
83 |
4
|
oveq2i |
|
84 |
83
|
oveq1i |
|
85 |
|
2cn |
|
86 |
|
2ne0 |
|
87 |
35 85 86
|
divcan4i |
|
88 |
84 87
|
eqtri |
|
89 |
82 88
|
eqtri |
|
90 |
80 89
|
eqtrdi |
|
91 |
|
oveq1 |
|
92 |
|
oveq2 |
|
93 |
92
|
oveq1d |
|
94 |
|
2p1e3 |
|
95 |
35 85 60 94
|
subaddrii |
|
96 |
95
|
oveq1i |
|
97 |
96 5
|
eqtr4i |
|
98 |
93 97
|
eqtrdi |
|
99 |
91 98
|
oveq12d |
|
100 |
90 99
|
oveq12d |
|
101 |
|
2nn0 |
|
102 |
|
bpolycl |
|
103 |
101 102
|
mpan |
|
104 |
|
2cnne0 |
|
105 |
|
div12 |
|
106 |
35 104 105
|
mp3an13 |
|
107 |
103 106
|
syl |
|
108 |
35 85 86
|
divcli |
|
109 |
|
mulcom |
|
110 |
103 108 109
|
sylancl |
|
111 |
|
bpoly2 |
|
112 |
111
|
oveq2d |
|
113 |
|
sqcl |
|
114 |
|
6cn |
|
115 |
|
6re |
|
116 |
|
6pos |
|
117 |
115 116
|
gt0ne0ii |
|
118 |
114 117
|
reccli |
|
119 |
|
subsub |
|
120 |
118 119
|
mp3an3 |
|
121 |
113 120
|
mpancom |
|
122 |
121
|
oveq2d |
|
123 |
|
subcl |
|
124 |
118 123
|
mpan2 |
|
125 |
|
subdi |
|
126 |
108 113 124 125
|
mp3an2i |
|
127 |
112 122 126
|
3eqtr2d |
|
128 |
107 110 127
|
3eqtrd |
|
129 |
100 128
|
sylan9eqr |
|
130 |
|
mulcl |
|
131 |
108 113 130
|
sylancr |
|
132 |
|
mulcl |
|
133 |
108 124 132
|
sylancr |
|
134 |
131 133
|
subcld |
|
135 |
134
|
adantr |
|
136 |
129 135
|
eqeltrd |
|
137 |
52 79 136
|
3jaodan |
|
138 |
27 137
|
sylan2b |
|
139 |
5
|
eqeq2i |
|
140 |
139 100
|
sylbir |
|
141 |
10 138 140
|
fsump1 |
|
142 |
128
|
oveq2d |
|
143 |
15
|
sumeq1i |
|
144 |
|
0nn0 |
|
145 |
|
nn0uz |
|
146 |
144 145
|
eleqtri |
|
147 |
146
|
a1i |
|
148 |
13 16
|
eqtri |
|
149 |
148
|
eleq2i |
|
150 |
25
|
elpr |
|
151 |
149 150
|
bitri |
|
152 |
52 79
|
jaodan |
|
153 |
151 152
|
sylan2b |
|
154 |
14
|
eqeq2i |
|
155 |
154 65
|
sylbi |
|
156 |
147 153 155
|
fsump1 |
|
157 |
50 48
|
eqeltrdi |
|
158 |
42
|
fsum1 |
|
159 |
11 157 158
|
sylancr |
|
160 |
159 50
|
eqtrd |
|
161 |
160 76
|
oveq12d |
|
162 |
156 161
|
eqtrd |
|
163 |
143 162
|
syl5eqr |
|
164 |
163
|
oveq1d |
|
165 |
|
addcl |
|
166 |
48 71 165
|
sylancr |
|
167 |
166 131 133
|
addsub12d |
|
168 |
164 167
|
eqtrd |
|
169 |
133 166
|
negsubdi2d |
|
170 |
|
subdi |
|
171 |
108 118 170
|
mp3an13 |
|
172 |
|
addsub12 |
|
173 |
48 69 172
|
mp3an13 |
|
174 |
171 173
|
oveq12d |
|
175 |
|
mulcl |
|
176 |
108 175
|
mpan |
|
177 |
108 118
|
mulcli |
|
178 |
|
negsub |
|
179 |
176 177 178
|
sylancl |
|
180 |
179
|
oveq1d |
|
181 |
69 48
|
negsubdi2i |
|
182 |
85 35 85
|
mul12i |
|
183 |
|
3t2e6 |
|
184 |
183
|
oveq2i |
|
185 |
|
2t2e4 |
|
186 |
185
|
oveq2i |
|
187 |
182 184 186
|
3eqtr3i |
|
188 |
187
|
oveq2i |
|
189 |
46 47
|
pm3.2i |
|
190 |
35 72
|
pm3.2i |
|
191 |
|
divcan5 |
|
192 |
60 189 190 191
|
mp3an |
|
193 |
188 192
|
eqtri |
|
194 |
35 85 60 114 86 117
|
divmuldivi |
|
195 |
|
2t1e2 |
|
196 |
195 5
|
eqtri |
|
197 |
196 185
|
oveq12i |
|
198 |
|
divcan5 |
|
199 |
60 104 104 198
|
mp3an |
|
200 |
60 60 46 47
|
divdiri |
|
201 |
197 199 200
|
3eqtr3ri |
|
202 |
69 48 48 201
|
subaddrii |
|
203 |
193 194 202
|
3eqtr4ri |
|
204 |
203
|
negeqi |
|
205 |
181 204
|
eqtr3i |
|
206 |
48 69
|
subcli |
|
207 |
177
|
negcli |
|
208 |
206 207
|
subeq0i |
|
209 |
205 208
|
mpbir |
|
210 |
209
|
oveq2i |
|
211 |
|
id |
|
212 |
206
|
a1i |
|
213 |
207
|
a1i |
|
214 |
176 211 212 213
|
subadd4d |
|
215 |
|
subdir |
|
216 |
108 60 215
|
mp3an12 |
|
217 |
|
divsubdir |
|
218 |
35 85 104 217
|
mp3an |
|
219 |
95
|
oveq1i |
|
220 |
|
2div2e1 |
|
221 |
220
|
oveq2i |
|
222 |
218 219 221
|
3eqtr3ri |
|
223 |
222
|
oveq1i |
|
224 |
223
|
a1i |
|
225 |
|
mulid2 |
|
226 |
225
|
oveq2d |
|
227 |
216 224 226
|
3eqtr3rd |
|
228 |
227
|
oveq1d |
|
229 |
|
mulcl |
|
230 |
69 229
|
mpan |
|
231 |
230
|
subid1d |
|
232 |
228 231
|
eqtrd |
|
233 |
210 214 232
|
3eqtr3a |
|
234 |
174 180 233
|
3eqtr2d |
|
235 |
234
|
negeqd |
|
236 |
169 235
|
eqtr3d |
|
237 |
236
|
oveq2d |
|
238 |
131 230
|
negsubd |
|
239 |
168 237 238
|
3eqtrd |
|
240 |
141 142 239
|
3eqtrd |
|
241 |
8 240
|
syl5eq |
|
242 |
241
|
oveq2d |
|
243 |
|
expcl |
|
244 |
1 243
|
mpan2 |
|
245 |
244 131 230
|
subsubd |
|
246 |
3 242 245
|
3eqtrd |
|