Step |
Hyp |
Ref |
Expression |
1 |
|
gsumhashmul.b |
|
2 |
|
gsumhashmul.z |
|
3 |
|
gsumhashmul.x |
|
4 |
|
gsumhashmul.g |
|
5 |
|
gsumhashmul.f |
|
6 |
|
gsumhashmul.1 |
|
7 |
|
suppssdm |
|
8 |
7 5
|
fssdm |
|
9 |
5 8
|
feqresmpt |
|
10 |
9
|
oveq2d |
|
11 |
|
relfsupp |
|
12 |
11
|
brrelex1i |
|
13 |
6 12
|
syl |
|
14 |
5
|
ffnd |
|
15 |
13 14
|
fndmexd |
|
16 |
|
ssidd |
|
17 |
1 2 4 15 5 16 6
|
gsumres |
|
18 |
|
nfcv |
|
19 |
|
fveq2 |
|
20 |
6
|
fsuppimpd |
|
21 |
|
ssidd |
|
22 |
5
|
adantr |
|
23 |
8
|
sselda |
|
24 |
22 23
|
ffvelrnd |
|
25 |
5
|
ffund |
|
26 |
|
funrel |
|
27 |
|
reldif |
|
28 |
25 26 27
|
3syl |
|
29 |
|
1stdm |
|
30 |
28 29
|
sylan |
|
31 |
2
|
fvexi |
|
32 |
31
|
a1i |
|
33 |
|
fressupp |
|
34 |
25 13 32 33
|
syl3anc |
|
35 |
34
|
dmeqd |
|
36 |
7
|
a1i |
|
37 |
|
ssdmres |
|
38 |
36 37
|
sylib |
|
39 |
35 38
|
eqtr3d |
|
40 |
39
|
adantr |
|
41 |
30 40
|
eleqtrd |
|
42 |
25
|
funresd |
|
43 |
42
|
adantr |
|
44 |
38
|
eleq2d |
|
45 |
44
|
biimpar |
|
46 |
|
simpr |
|
47 |
46
|
fvresd |
|
48 |
|
funopfvb |
|
49 |
48
|
biimpa |
|
50 |
43 45 47 49
|
syl21anc |
|
51 |
34
|
adantr |
|
52 |
50 51
|
eleqtrd |
|
53 |
|
eqeq2 |
|
54 |
53
|
bibi2d |
|
55 |
54
|
ralbidv |
|
56 |
55
|
adantl |
|
57 |
|
fvexd |
|
58 |
28
|
ad3antrrr |
|
59 |
|
simplr |
|
60 |
|
1st2nd |
|
61 |
58 59 60
|
syl2anc |
|
62 |
|
opeq1 |
|
63 |
62
|
adantl |
|
64 |
61 63
|
eqtr4d |
|
65 |
|
difssd |
|
66 |
65
|
sselda |
|
67 |
66
|
adantr |
|
68 |
64 67
|
eqeltrrd |
|
69 |
64 68
|
jca |
|
70 |
|
opeq2 |
|
71 |
70
|
eqeq2d |
|
72 |
70
|
eleq1d |
|
73 |
71 72
|
anbi12d |
|
74 |
57 69 73
|
spcedv |
|
75 |
|
vex |
|
76 |
75
|
elsnres |
|
77 |
74 76
|
sylibr |
|
78 |
14
|
ad3antrrr |
|
79 |
23
|
ad2antrr |
|
80 |
|
fnressn |
|
81 |
78 79 80
|
syl2anc |
|
82 |
77 81
|
eleqtrd |
|
83 |
|
elsni |
|
84 |
82 83
|
syl |
|
85 |
|
simpr |
|
86 |
85
|
fveq2d |
|
87 |
|
fvex |
|
88 |
75 87
|
op1st |
|
89 |
86 88
|
eqtr2di |
|
90 |
84 89
|
impbida |
|
91 |
90
|
ralrimiva |
|
92 |
52 56 91
|
rspcedvd |
|
93 |
|
reu6 |
|
94 |
92 93
|
sylibr |
|
95 |
18 1 2 19 4 20 21 24 41 94
|
gsummptf1o |
|
96 |
10 17 95
|
3eqtr3d |
|
97 |
|
simpr |
|
98 |
97
|
eldifad |
|
99 |
|
funfv1st2nd |
|
100 |
25 98 99
|
syl2an2r |
|
101 |
100
|
mpteq2dva |
|
102 |
101
|
oveq2d |
|
103 |
96 102
|
eqtrd |
|
104 |
|
nfcv |
|
105 |
|
fvex |
|
106 |
|
fvex |
|
107 |
105 106
|
op2ndd |
|
108 |
|
resfnfinfin |
|
109 |
14 20 108
|
syl2anc |
|
110 |
34 109
|
eqeltrrd |
|
111 |
34
|
rneqd |
|
112 |
|
rnresss |
|
113 |
5
|
frnd |
|
114 |
112 113
|
sstrid |
|
115 |
111 114
|
eqsstrrd |
|
116 |
|
2ndrn |
|
117 |
28 116
|
sylan |
|
118 |
|
relcnv |
|
119 |
|
reldif |
|
120 |
118 119
|
mp1i |
|
121 |
|
1st2nd |
|
122 |
120 121
|
sylan |
|
123 |
|
cnvdif |
|
124 |
|
cnvxp |
|
125 |
124
|
difeq2i |
|
126 |
123 125
|
eqtri |
|
127 |
126
|
eqimss2i |
|
128 |
127
|
a1i |
|
129 |
128
|
sselda |
|
130 |
122 129
|
eqeltrrd |
|
131 |
106 105
|
opelcnv |
|
132 |
130 131
|
sylib |
|
133 |
28
|
adantr |
|
134 |
|
eqidd |
|
135 |
|
cnvf1olem |
|
136 |
135
|
simpld |
|
137 |
133 97 134 136
|
syl12anc |
|
138 |
137 126
|
eleqtrdi |
|
139 |
|
eqeq2 |
|
140 |
139
|
bibi2d |
|
141 |
140
|
ralbidv |
|
142 |
141
|
adantl |
|
143 |
118 119
|
mp1i |
|
144 |
|
simplr |
|
145 |
|
simpr |
|
146 |
|
df-rel |
|
147 |
120 146
|
sylib |
|
148 |
147
|
ad3antrrr |
|
149 |
148 144
|
sseldd |
|
150 |
|
2nd1st |
|
151 |
149 150
|
syl |
|
152 |
145 151
|
eqtr4d |
|
153 |
|
cnvf1olem |
|
154 |
153
|
simprd |
|
155 |
143 144 152 154
|
syl12anc |
|
156 |
28
|
ad3antrrr |
|
157 |
97
|
ad2antrr |
|
158 |
|
simpr |
|
159 |
|
cnvf1olem |
|
160 |
159
|
simprd |
|
161 |
156 157 158 160
|
syl12anc |
|
162 |
147
|
ad3antrrr |
|
163 |
|
simplr |
|
164 |
162 163
|
sseldd |
|
165 |
164 150
|
syl |
|
166 |
161 165
|
eqtrd |
|
167 |
155 166
|
impbida |
|
168 |
167
|
ralrimiva |
|
169 |
138 142 168
|
rspcedvd |
|
170 |
|
reu6 |
|
171 |
169 170
|
sylibr |
|
172 |
104 1 2 107 4 110 115 117 132 171
|
gsummptf1o |
|
173 |
|
fveq2 |
|
174 |
173
|
cbvmptv |
|
175 |
34
|
cnveqd |
|
176 |
175 126
|
eqtr2di |
|
177 |
176
|
mpteq1d |
|
178 |
174 177
|
syl5eq |
|
179 |
178
|
oveq2d |
|
180 |
103 172 179
|
3eqtrd |
|
181 |
|
nfcv |
|
182 |
|
nfv |
|
183 |
|
vex |
|
184 |
75 183
|
op1std |
|
185 |
|
relcnv |
|
186 |
185
|
a1i |
|
187 |
|
cnvfi |
|
188 |
109 187
|
syl |
|
189 |
113
|
adantr |
|
190 |
185
|
a1i |
|
191 |
|
simpr |
|
192 |
|
1stdm |
|
193 |
190 191 192
|
syl2anc |
|
194 |
|
df-rn |
|
195 |
193 194
|
eleqtrrdi |
|
196 |
112 195
|
sselid |
|
197 |
189 196
|
sseldd |
|
198 |
181 182 1 184 186 188 4 197
|
gsummpt2d |
|
199 |
|
df-ima |
|
200 |
|
supppreima |
|
201 |
25 13 32 200
|
syl3anc |
|
202 |
201
|
imaeq2d |
|
203 |
199 202
|
eqtr3id |
|
204 |
|
funimacnv |
|
205 |
25 204
|
syl |
|
206 |
|
difssd |
|
207 |
|
df-ss |
|
208 |
206 207
|
sylib |
|
209 |
203 205 208
|
3eqtrd |
|
210 |
194 209
|
eqtr3id |
|
211 |
4
|
cmnmndd |
|
212 |
211
|
adantr |
|
213 |
109
|
adantr |
|
214 |
|
imafi2 |
|
215 |
213 187 214
|
3syl |
|
216 |
194 114
|
eqsstrrid |
|
217 |
216
|
sselda |
|
218 |
1 3
|
gsumconst |
|
219 |
212 215 217 218
|
syl3anc |
|
220 |
|
cnvresima |
|
221 |
210
|
eleq2d |
|
222 |
221
|
biimpa |
|
223 |
222
|
snssd |
|
224 |
|
sspreima |
|
225 |
25 223 224
|
syl2an2r |
|
226 |
201
|
adantr |
|
227 |
225 226
|
sseqtrrd |
|
228 |
|
df-ss |
|
229 |
227 228
|
sylib |
|
230 |
220 229
|
eqtr2id |
|
231 |
230
|
fveq2d |
|
232 |
231
|
oveq1d |
|
233 |
219 232
|
eqtr4d |
|
234 |
210 233
|
mpteq12dva |
|
235 |
234
|
oveq2d |
|
236 |
180 198 235
|
3eqtrd |
|