Step |
Hyp |
Ref |
Expression |
1 |
|
gsumzadd.b |
|
2 |
|
gsumzadd.0 |
|
3 |
|
gsumzadd.p |
|
4 |
|
gsumzadd.z |
|
5 |
|
gsumzadd.g |
|
6 |
|
gsumzadd.a |
|
7 |
|
gsumzadd.fn |
|
8 |
|
gsumzadd.hn |
|
9 |
|
gsumzaddlem.w |
|
10 |
|
gsumzaddlem.f |
|
11 |
|
gsumzaddlem.h |
|
12 |
|
gsumzaddlem.1 |
|
13 |
|
gsumzaddlem.2 |
|
14 |
|
gsumzaddlem.3 |
|
15 |
|
gsumzaddlem.4 |
|
16 |
1 2
|
mndidcl |
|
17 |
5 16
|
syl |
|
18 |
1 3 2
|
mndlid |
|
19 |
5 17 18
|
syl2anc |
|
20 |
19
|
adantr |
|
21 |
2
|
fvexi |
|
22 |
21
|
a1i |
|
23 |
|
fex |
|
24 |
11 6 23
|
syl2anc |
|
25 |
24
|
suppun |
|
26 |
25 9
|
sseqtrrdi |
|
27 |
10 6 22 26
|
gsumcllem |
|
28 |
27
|
oveq2d |
|
29 |
2
|
gsumz |
|
30 |
5 6 29
|
syl2anc |
|
31 |
30
|
adantr |
|
32 |
28 31
|
eqtrd |
|
33 |
|
fex |
|
34 |
10 6 33
|
syl2anc |
|
35 |
34
|
suppun |
|
36 |
|
uncom |
|
37 |
36
|
oveq1i |
|
38 |
35 37
|
sseqtrrdi |
|
39 |
38 9
|
sseqtrrdi |
|
40 |
11 6 22 39
|
gsumcllem |
|
41 |
40
|
oveq2d |
|
42 |
41 31
|
eqtrd |
|
43 |
32 42
|
oveq12d |
|
44 |
6
|
adantr |
|
45 |
17
|
ad2antrr |
|
46 |
44 45 45 27 40
|
offval2 |
|
47 |
20
|
mpteq2dv |
|
48 |
46 47
|
eqtrd |
|
49 |
48
|
oveq2d |
|
50 |
49 31
|
eqtrd |
|
51 |
20 43 50
|
3eqtr4rd |
|
52 |
51
|
ex |
|
53 |
5
|
adantr |
|
54 |
1 3
|
mndcl |
|
55 |
54
|
3expb |
|
56 |
53 55
|
sylan |
|
57 |
56
|
caovclg |
|
58 |
|
simprl |
|
59 |
|
nnuz |
|
60 |
58 59
|
eleqtrdi |
|
61 |
10
|
adantr |
|
62 |
|
f1of1 |
|
63 |
62
|
ad2antll |
|
64 |
|
suppssdm |
|
65 |
64
|
a1i |
|
66 |
9
|
a1i |
|
67 |
|
dmun |
|
68 |
10
|
fdmd |
|
69 |
11
|
fdmd |
|
70 |
68 69
|
uneq12d |
|
71 |
|
unidm |
|
72 |
70 71
|
eqtrdi |
|
73 |
67 72
|
syl5req |
|
74 |
65 66 73
|
3sstr4d |
|
75 |
74
|
adantr |
|
76 |
|
f1ss |
|
77 |
63 75 76
|
syl2anc |
|
78 |
|
f1f |
|
79 |
77 78
|
syl |
|
80 |
|
fco |
|
81 |
61 79 80
|
syl2anc |
|
82 |
81
|
ffvelrnda |
|
83 |
11
|
adantr |
|
84 |
|
fco |
|
85 |
83 79 84
|
syl2anc |
|
86 |
85
|
ffvelrnda |
|
87 |
61
|
ffnd |
|
88 |
83
|
ffnd |
|
89 |
6
|
adantr |
|
90 |
|
ovexd |
|
91 |
|
inidm |
|
92 |
87 88 79 89 89 90 91
|
ofco |
|
93 |
92
|
fveq1d |
|
94 |
93
|
adantr |
|
95 |
|
fnfco |
|
96 |
87 79 95
|
syl2anc |
|
97 |
|
fnfco |
|
98 |
88 79 97
|
syl2anc |
|
99 |
|
inidm |
|
100 |
|
eqidd |
|
101 |
|
eqidd |
|
102 |
96 98 90 90 99 100 101
|
ofval |
|
103 |
94 102
|
eqtrd |
|
104 |
5
|
ad2antrr |
|
105 |
|
elfzouz |
|
106 |
105
|
adantl |
|
107 |
|
elfzouz2 |
|
108 |
107
|
adantl |
|
109 |
|
fzss2 |
|
110 |
108 109
|
syl |
|
111 |
110
|
sselda |
|
112 |
82
|
adantlr |
|
113 |
111 112
|
syldan |
|
114 |
1 3
|
mndcl |
|
115 |
114
|
3expb |
|
116 |
104 115
|
sylan |
|
117 |
106 113 116
|
seqcl |
|
118 |
86
|
adantlr |
|
119 |
111 118
|
syldan |
|
120 |
106 119 116
|
seqcl |
|
121 |
|
fzofzp1 |
|
122 |
|
ffvelrn |
|
123 |
81 121 122
|
syl2an |
|
124 |
|
ffvelrn |
|
125 |
85 121 124
|
syl2an |
|
126 |
|
fvco3 |
|
127 |
79 121 126
|
syl2an |
|
128 |
|
fveq2 |
|
129 |
128
|
eleq1d |
|
130 |
15
|
expr |
|
131 |
130
|
ralrimiv |
|
132 |
131
|
ex |
|
133 |
132
|
alrimiv |
|
134 |
133
|
ad2antrr |
|
135 |
|
imassrn |
|
136 |
79
|
adantr |
|
137 |
136
|
frnd |
|
138 |
135 137
|
sstrid |
|
139 |
|
vex |
|
140 |
139
|
imaex |
|
141 |
|
sseq1 |
|
142 |
|
difeq2 |
|
143 |
|
reseq2 |
|
144 |
143
|
oveq2d |
|
145 |
144
|
sneqd |
|
146 |
145
|
fveq2d |
|
147 |
146
|
eleq2d |
|
148 |
142 147
|
raleqbidv |
|
149 |
141 148
|
imbi12d |
|
150 |
140 149
|
spcv |
|
151 |
134 138 150
|
sylc |
|
152 |
|
ffvelrn |
|
153 |
79 121 152
|
syl2an |
|
154 |
|
fzp1nel |
|
155 |
77
|
adantr |
|
156 |
121
|
adantl |
|
157 |
|
f1elima |
|
158 |
155 156 110 157
|
syl3anc |
|
159 |
154 158
|
mtbiri |
|
160 |
153 159
|
eldifd |
|
161 |
129 151 160
|
rspcdva |
|
162 |
127 161
|
eqeltrd |
|
163 |
140
|
a1i |
|
164 |
11
|
ad2antrr |
|
165 |
164 138
|
fssresd |
|
166 |
13
|
ad2antrr |
|
167 |
|
resss |
|
168 |
167
|
rnssi |
|
169 |
4
|
cntzidss |
|
170 |
166 168 169
|
sylancl |
|
171 |
106 59
|
eleqtrrdi |
|
172 |
|
f1ores |
|
173 |
155 110 172
|
syl2anc |
|
174 |
|
f1of1 |
|
175 |
173 174
|
syl |
|
176 |
|
suppssdm |
|
177 |
|
dmres |
|
178 |
177
|
a1i |
|
179 |
176 178
|
sseqtrid |
|
180 |
|
inss1 |
|
181 |
|
df-ima |
|
182 |
181
|
a1i |
|
183 |
180 182
|
sseqtrid |
|
184 |
179 183
|
sstrd |
|
185 |
|
eqid |
|
186 |
1 2 3 4 104 163 165 170 171 175 184 185
|
gsumval3 |
|
187 |
181
|
eqimss2i |
|
188 |
|
cores |
|
189 |
187 188
|
ax-mp |
|
190 |
|
resco |
|
191 |
189 190
|
eqtr4i |
|
192 |
191
|
fveq1i |
|
193 |
|
fvres |
|
194 |
192 193
|
syl5eq |
|
195 |
194
|
adantl |
|
196 |
106 195
|
seqfveq |
|
197 |
186 196
|
eqtr2d |
|
198 |
|
fvex |
|
199 |
198
|
elsn |
|
200 |
197 199
|
sylibr |
|
201 |
3 4
|
cntzi |
|
202 |
162 200 201
|
syl2anc |
|
203 |
202
|
eqcomd |
|
204 |
1 3 104 117 120 123 125 203
|
mnd4g |
|
205 |
57 57 60 82 86 103 204
|
seqcaopr3 |
|
206 |
56 61 83 89 89 91
|
off |
|
207 |
14
|
adantr |
|
208 |
53 115
|
sylan |
|
209 |
208 61 83 89 89 91
|
off |
|
210 |
|
eldifi |
|
211 |
|
eqidd |
|
212 |
|
eqidd |
|
213 |
87 88 89 89 91 211 212
|
ofval |
|
214 |
210 213
|
sylan2 |
|
215 |
25
|
adantr |
|
216 |
|
f1ofo |
|
217 |
|
forn |
|
218 |
216 217
|
syl |
|
219 |
218 9
|
eqtrdi |
|
220 |
219
|
sseq2d |
|
221 |
220
|
ad2antll |
|
222 |
215 221
|
mpbird |
|
223 |
21
|
a1i |
|
224 |
61 222 89 223
|
suppssr |
|
225 |
35
|
adantr |
|
226 |
225 37
|
sseqtrrdi |
|
227 |
219
|
sseq2d |
|
228 |
227
|
ad2antll |
|
229 |
226 228
|
mpbird |
|
230 |
83 229 89 223
|
suppssr |
|
231 |
224 230
|
oveq12d |
|
232 |
19
|
ad2antrr |
|
233 |
214 231 232
|
3eqtrd |
|
234 |
209 233
|
suppss |
|
235 |
|
ovex |
|
236 |
235 139
|
coex |
|
237 |
|
suppimacnv |
|
238 |
237
|
eqcomd |
|
239 |
236 21 238
|
mp2an |
|
240 |
1 2 3 4 53 89 206 207 58 77 234 239
|
gsumval3 |
|
241 |
12
|
adantr |
|
242 |
|
eqid |
|
243 |
1 2 3 4 53 89 61 241 58 77 222 242
|
gsumval3 |
|
244 |
13
|
adantr |
|
245 |
|
eqid |
|
246 |
1 2 3 4 53 89 83 244 58 77 229 245
|
gsumval3 |
|
247 |
243 246
|
oveq12d |
|
248 |
205 240 247
|
3eqtr4d |
|
249 |
248
|
expr |
|
250 |
249
|
exlimdv |
|
251 |
250
|
expimpd |
|
252 |
7 8
|
fsuppun |
|
253 |
9 252
|
eqeltrid |
|
254 |
|
fz1f1o |
|
255 |
253 254
|
syl |
|
256 |
52 251 255
|
mpjaod |
|