Step |
Hyp |
Ref |
Expression |
1 |
|
rpvmasum.z |
|
2 |
|
rpvmasum.l |
|
3 |
|
rpvmasum.a |
|
4 |
|
rpvmasum2.g |
|
5 |
|
rpvmasum2.d |
|
6 |
|
rpvmasum2.1 |
|
7 |
|
dchrisum0f.f |
|
8 |
|
dchrisum0f.x |
|
9 |
|
dchrisum0flb.r |
|
10 |
|
dchrisum0flblem1.1 |
|
11 |
|
dchrisum0flblem1.2 |
|
12 |
|
1red |
|
13 |
|
0red |
|
14 |
12 13
|
ifclda |
|
15 |
|
1red |
|
16 |
|
fzfid |
|
17 |
3
|
nnnn0d |
|
18 |
|
eqid |
|
19 |
1 18 2
|
znzrhfo |
|
20 |
|
fof |
|
21 |
17 19 20
|
3syl |
|
22 |
|
prmz |
|
23 |
10 22
|
syl |
|
24 |
21 23
|
ffvelrnd |
|
25 |
9 24
|
ffvelrnd |
|
26 |
|
elfznn0 |
|
27 |
|
reexpcl |
|
28 |
25 26 27
|
syl2an |
|
29 |
16 28
|
fsumrecl |
|
30 |
29
|
adantr |
|
31 |
|
breq1 |
|
32 |
|
breq1 |
|
33 |
|
1le1 |
|
34 |
|
0le1 |
|
35 |
31 32 33 34
|
keephyp |
|
36 |
35
|
a1i |
|
37 |
|
nn0uz |
|
38 |
11 37
|
eleqtrdi |
|
39 |
|
fzn0 |
|
40 |
38 39
|
sylibr |
|
41 |
|
hashnncl |
|
42 |
16 41
|
syl |
|
43 |
40 42
|
mpbird |
|
44 |
43
|
adantr |
|
45 |
44
|
nnge1d |
|
46 |
|
simpr |
|
47 |
46
|
oveq1d |
|
48 |
|
elfzelz |
|
49 |
|
1exp |
|
50 |
48 49
|
syl |
|
51 |
47 50
|
sylan9eq |
|
52 |
51
|
sumeq2dv |
|
53 |
|
fzfid |
|
54 |
|
ax-1cn |
|
55 |
|
fsumconst |
|
56 |
53 54 55
|
sylancl |
|
57 |
44
|
nncnd |
|
58 |
57
|
mulid1d |
|
59 |
52 56 58
|
3eqtrd |
|
60 |
45 59
|
breqtrrd |
|
61 |
14 15 30 36 60
|
letrd |
|
62 |
|
oveq1 |
|
63 |
62
|
breq1d |
|
64 |
|
oveq1 |
|
65 |
64
|
breq1d |
|
66 |
|
1re |
|
67 |
25
|
adantr |
|
68 |
|
resubcl |
|
69 |
66 67 68
|
sylancr |
|
70 |
69
|
adantr |
|
71 |
70
|
leidd |
|
72 |
69
|
recnd |
|
73 |
72
|
adantr |
|
74 |
73
|
mulid2d |
|
75 |
|
nn0p1nn |
|
76 |
11 75
|
syl |
|
77 |
76
|
ad3antrrr |
|
78 |
77
|
0expd |
|
79 |
|
simpr |
|
80 |
79
|
oveq1d |
|
81 |
78 80 79
|
3eqtr4d |
|
82 |
|
neg1cn |
|
83 |
11
|
ad2antrr |
|
84 |
|
expp1 |
|
85 |
82 83 84
|
sylancr |
|
86 |
|
prmnn |
|
87 |
10 86
|
syl |
|
88 |
87 11
|
nnexpcld |
|
89 |
88
|
nncnd |
|
90 |
89
|
ad2antrr |
|
91 |
90
|
sqsqrtd |
|
92 |
91
|
oveq2d |
|
93 |
10
|
ad2antrr |
|
94 |
|
nnq |
|
95 |
94
|
adantl |
|
96 |
|
nnne0 |
|
97 |
96
|
adantl |
|
98 |
|
2z |
|
99 |
98
|
a1i |
|
100 |
|
pcexp |
|
101 |
93 95 97 99 100
|
syl121anc |
|
102 |
83
|
nn0zd |
|
103 |
|
pcid |
|
104 |
93 102 103
|
syl2anc |
|
105 |
92 101 104
|
3eqtr3rd |
|
106 |
105
|
oveq2d |
|
107 |
82
|
a1i |
|
108 |
|
simpr |
|
109 |
93 108
|
pccld |
|
110 |
|
2nn0 |
|
111 |
110
|
a1i |
|
112 |
107 109 111
|
expmuld |
|
113 |
|
neg1sqe1 |
|
114 |
113
|
oveq1i |
|
115 |
109
|
nn0zd |
|
116 |
|
1exp |
|
117 |
115 116
|
syl |
|
118 |
114 117
|
syl5eq |
|
119 |
106 112 118
|
3eqtrd |
|
120 |
119
|
oveq1d |
|
121 |
82
|
mulid2i |
|
122 |
120 121
|
eqtrdi |
|
123 |
85 122
|
eqtrd |
|
124 |
123
|
adantr |
|
125 |
25
|
recnd |
|
126 |
125
|
adantr |
|
127 |
126
|
ad2antrr |
|
128 |
127
|
negnegd |
|
129 |
|
simpr |
|
130 |
129
|
ad2antrr |
|
131 |
8
|
ad3antrrr |
|
132 |
|
eqid |
|
133 |
4 1 5 18 132 8 24
|
dchrn0 |
|
134 |
133
|
ad2antrr |
|
135 |
134
|
biimpa |
|
136 |
4 5 131 1 132 135
|
dchrabs |
|
137 |
|
eqeq1 |
|
138 |
136 137
|
syl5ibcom |
|
139 |
138
|
necon3ad |
|
140 |
130 139
|
mpd |
|
141 |
67
|
ad2antrr |
|
142 |
141
|
absord |
|
143 |
142
|
ord |
|
144 |
140 143
|
mpd |
|
145 |
144 136
|
eqtr3d |
|
146 |
145
|
negeqd |
|
147 |
128 146
|
eqtr3d |
|
148 |
147
|
oveq1d |
|
149 |
124 148 147
|
3eqtr4d |
|
150 |
81 149
|
pm2.61dane |
|
151 |
150
|
oveq2d |
|
152 |
71 74 151
|
3brtr4d |
|
153 |
72
|
mul02d |
|
154 |
|
peano2nn0 |
|
155 |
11 154
|
syl |
|
156 |
25 155
|
reexpcld |
|
157 |
156
|
adantr |
|
158 |
157
|
recnd |
|
159 |
158
|
abscld |
|
160 |
|
1red |
|
161 |
157
|
leabsd |
|
162 |
155
|
adantr |
|
163 |
126 162
|
absexpd |
|
164 |
126
|
abscld |
|
165 |
126
|
absge0d |
|
166 |
4 5 1 18 8 24
|
dchrabs2 |
|
167 |
166
|
adantr |
|
168 |
|
exple1 |
|
169 |
164 165 167 162 168
|
syl31anc |
|
170 |
163 169
|
eqbrtrd |
|
171 |
157 159 160 161 170
|
letrd |
|
172 |
|
subge0 |
|
173 |
66 157 172
|
sylancr |
|
174 |
171 173
|
mpbird |
|
175 |
153 174
|
eqbrtrd |
|
176 |
175
|
adantr |
|
177 |
63 65 152 176
|
ifbothda |
|
178 |
|
0re |
|
179 |
66 178
|
ifcli |
|
180 |
179
|
a1i |
|
181 |
|
resubcl |
|
182 |
66 157 181
|
sylancr |
|
183 |
67
|
leabsd |
|
184 |
67 164 160 183 167
|
letrd |
|
185 |
129
|
necomd |
|
186 |
67 160 184 185
|
leneltd |
|
187 |
|
posdif |
|
188 |
67 66 187
|
sylancl |
|
189 |
186 188
|
mpbid |
|
190 |
|
lemuldiv |
|
191 |
180 182 69 189 190
|
syl112anc |
|
192 |
177 191
|
mpbid |
|
193 |
11
|
nn0zd |
|
194 |
|
fzval3 |
|
195 |
193 194
|
syl |
|
196 |
195
|
adantr |
|
197 |
196
|
sumeq1d |
|
198 |
|
0nn0 |
|
199 |
198
|
a1i |
|
200 |
155 37
|
eleqtrdi |
|
201 |
200
|
adantr |
|
202 |
126 129 199 201
|
geoserg |
|
203 |
126
|
exp0d |
|
204 |
203
|
oveq1d |
|
205 |
204
|
oveq1d |
|
206 |
197 202 205
|
3eqtrd |
|
207 |
192 206
|
breqtrrd |
|
208 |
61 207
|
pm2.61dane |
|
209 |
1 2 3 4 5 6 7
|
dchrisum0fval |
|
210 |
88 209
|
syl |
|
211 |
|
2fveq3 |
|
212 |
|
eqid |
|
213 |
212
|
dvdsppwf1o |
|
214 |
10 11 213
|
syl2anc |
|
215 |
|
oveq2 |
|
216 |
|
ovex |
|
217 |
215 212 216
|
fvmpt3i |
|
218 |
217
|
adantl |
|
219 |
9
|
adantr |
|
220 |
|
elrabi |
|
221 |
220
|
nnzd |
|
222 |
|
ffvelrn |
|
223 |
21 221 222
|
syl2an |
|
224 |
219 223
|
ffvelrnd |
|
225 |
224
|
recnd |
|
226 |
211 16 214 218 225
|
fsumf1o |
|
227 |
|
zsubrg |
|
228 |
|
eqid |
|
229 |
228
|
subrgsubm |
|
230 |
227 229
|
mp1i |
|
231 |
26
|
adantl |
|
232 |
23
|
adantr |
|
233 |
|
eqid |
|
234 |
|
zringmpg |
|
235 |
234
|
eqcomi |
|
236 |
|
eqid |
|
237 |
233 235 236
|
submmulg |
|
238 |
230 231 232 237
|
syl3anc |
|
239 |
87
|
nncnd |
|
240 |
|
cnfldexp |
|
241 |
239 26 240
|
syl2an |
|
242 |
238 241
|
eqtr3d |
|
243 |
242
|
fveq2d |
|
244 |
1
|
zncrng |
|
245 |
|
crngring |
|
246 |
17 244 245
|
3syl |
|
247 |
2
|
zrhrhm |
|
248 |
|
eqid |
|
249 |
|
eqid |
|
250 |
248 249
|
rhmmhm |
|
251 |
246 247 250
|
3syl |
|
252 |
251
|
adantr |
|
253 |
|
zringbas |
|
254 |
248 253
|
mgpbas |
|
255 |
|
eqid |
|
256 |
254 236 255
|
mhmmulg |
|
257 |
252 231 232 256
|
syl3anc |
|
258 |
243 257
|
eqtr3d |
|
259 |
258
|
fveq2d |
|
260 |
4 1 5
|
dchrmhm |
|
261 |
260 8
|
sseldi |
|
262 |
261
|
adantr |
|
263 |
24
|
adantr |
|
264 |
249 18
|
mgpbas |
|
265 |
264 255 233
|
mhmmulg |
|
266 |
262 231 263 265
|
syl3anc |
|
267 |
|
cnfldexp |
|
268 |
125 26 267
|
syl2an |
|
269 |
259 266 268
|
3eqtrd |
|
270 |
269
|
sumeq2dv |
|
271 |
210 226 270
|
3eqtrd |
|
272 |
208 271
|
breqtrrd |
|