Step |
Hyp |
Ref |
Expression |
1 |
|
gsum2d.b |
|
2 |
|
gsum2d.z |
|
3 |
|
gsum2d.g |
|
4 |
|
gsum2d.a |
|
5 |
|
gsum2d.r |
|
6 |
|
gsum2d.d |
|
7 |
|
gsum2d.s |
|
8 |
|
gsum2d.f |
|
9 |
|
gsum2d.w |
|
10 |
9
|
fsuppimpd |
|
11 |
|
dmfi |
|
12 |
10 11
|
syl |
|
13 |
|
reseq2 |
|
14 |
|
res0 |
|
15 |
13 14
|
eqtrdi |
|
16 |
15
|
reseq2d |
|
17 |
|
res0 |
|
18 |
16 17
|
eqtrdi |
|
19 |
18
|
oveq2d |
|
20 |
|
mpteq1 |
|
21 |
|
mpt0 |
|
22 |
20 21
|
eqtrdi |
|
23 |
22
|
oveq2d |
|
24 |
19 23
|
eqeq12d |
|
25 |
24
|
imbi2d |
|
26 |
|
reseq2 |
|
27 |
26
|
reseq2d |
|
28 |
27
|
oveq2d |
|
29 |
|
mpteq1 |
|
30 |
29
|
oveq2d |
|
31 |
28 30
|
eqeq12d |
|
32 |
31
|
imbi2d |
|
33 |
|
reseq2 |
|
34 |
33
|
reseq2d |
|
35 |
34
|
oveq2d |
|
36 |
|
mpteq1 |
|
37 |
36
|
oveq2d |
|
38 |
35 37
|
eqeq12d |
|
39 |
38
|
imbi2d |
|
40 |
|
reseq2 |
|
41 |
40
|
reseq2d |
|
42 |
41
|
oveq2d |
|
43 |
|
mpteq1 |
|
44 |
43
|
oveq2d |
|
45 |
42 44
|
eqeq12d |
|
46 |
45
|
imbi2d |
|
47 |
|
eqidd |
|
48 |
|
oveq1 |
|
49 |
|
eqid |
|
50 |
3
|
adantr |
|
51 |
|
resexg |
|
52 |
4 51
|
syl |
|
53 |
52
|
adantr |
|
54 |
|
resss |
|
55 |
|
fssres |
|
56 |
8 54 55
|
sylancl |
|
57 |
56
|
adantr |
|
58 |
8
|
ffund |
|
59 |
|
funres |
|
60 |
58 59
|
syl |
|
61 |
60
|
adantr |
|
62 |
10
|
adantr |
|
63 |
|
fex |
|
64 |
8 4 63
|
syl2anc |
|
65 |
2
|
fvexi |
|
66 |
|
ressuppss |
|
67 |
64 65 66
|
sylancl |
|
68 |
67
|
adantr |
|
69 |
62 68
|
ssfid |
|
70 |
|
resexg |
|
71 |
64 70
|
syl |
|
72 |
|
isfsupp |
|
73 |
71 65 72
|
sylancl |
|
74 |
73
|
adantr |
|
75 |
61 69 74
|
mpbir2and |
|
76 |
|
simprr |
|
77 |
|
disjsn |
|
78 |
76 77
|
sylibr |
|
79 |
78
|
reseq2d |
|
80 |
|
resindi |
|
81 |
79 80 14
|
3eqtr3g |
|
82 |
|
resundi |
|
83 |
82
|
a1i |
|
84 |
1 2 49 50 53 57 75 81 83
|
gsumsplit |
|
85 |
|
ssun1 |
|
86 |
|
ssres2 |
|
87 |
|
resabs1 |
|
88 |
85 86 87
|
mp2b |
|
89 |
88
|
oveq2i |
|
90 |
|
ssun2 |
|
91 |
|
ssres2 |
|
92 |
|
resabs1 |
|
93 |
90 91 92
|
mp2b |
|
94 |
93
|
oveq2i |
|
95 |
89 94
|
oveq12i |
|
96 |
84 95
|
eqtrdi |
|
97 |
|
simprl |
|
98 |
1 2 3 4 5 6 7 8 9
|
gsum2dlem1 |
|
99 |
98
|
ad2antrr |
|
100 |
|
vex |
|
101 |
100
|
a1i |
|
102 |
|
sneq |
|
103 |
102
|
imaeq2d |
|
104 |
|
oveq1 |
|
105 |
103 104
|
mpteq12dv |
|
106 |
105
|
oveq2d |
|
107 |
106
|
eleq1d |
|
108 |
107
|
imbi2d |
|
109 |
108 98
|
chvarvv |
|
110 |
109
|
adantr |
|
111 |
1 49 50 97 99 101 76 110 106
|
gsumunsn |
|
112 |
102
|
reseq2d |
|
113 |
112
|
reseq2d |
|
114 |
113
|
oveq2d |
|
115 |
106 114
|
eqeq12d |
|
116 |
115
|
imbi2d |
|
117 |
|
imaexg |
|
118 |
4 117
|
syl |
|
119 |
|
vex |
|
120 |
|
vex |
|
121 |
119 120
|
elimasn |
|
122 |
|
df-ov |
|
123 |
8
|
ffvelrnda |
|
124 |
122 123
|
eqeltrid |
|
125 |
121 124
|
sylan2b |
|
126 |
125
|
fmpttd |
|
127 |
|
funmpt |
|
128 |
127
|
a1i |
|
129 |
|
rnfi |
|
130 |
10 129
|
syl |
|
131 |
121
|
biimpi |
|
132 |
119 120
|
opelrn |
|
133 |
132
|
con3i |
|
134 |
131 133
|
anim12i |
|
135 |
|
eldif |
|
136 |
|
eldif |
|
137 |
134 135 136
|
3imtr4i |
|
138 |
|
ssidd |
|
139 |
65
|
a1i |
|
140 |
8 138 4 139
|
suppssr |
|
141 |
122 140
|
syl5eq |
|
142 |
137 141
|
sylan2 |
|
143 |
142 118
|
suppss2 |
|
144 |
130 143
|
ssfid |
|
145 |
118
|
mptexd |
|
146 |
|
isfsupp |
|
147 |
145 65 146
|
sylancl |
|
148 |
128 144 147
|
mpbir2and |
|
149 |
|
2ndconst |
|
150 |
119 149
|
mp1i |
|
151 |
1 2 3 118 126 148 150
|
gsumf1o |
|
152 |
|
1st2nd2 |
|
153 |
|
xp1st |
|
154 |
|
elsni |
|
155 |
153 154
|
syl |
|
156 |
155
|
opeq1d |
|
157 |
152 156
|
eqtrd |
|
158 |
157
|
fveq2d |
|
159 |
|
df-ov |
|
160 |
158 159
|
eqtr4di |
|
161 |
160
|
mpteq2ia |
|
162 |
8
|
feqmptd |
|
163 |
162
|
reseq1d |
|
164 |
|
resss |
|
165 |
|
resmpt |
|
166 |
164 165
|
ax-mp |
|
167 |
|
ressn |
|
168 |
167
|
mpteq1i |
|
169 |
166 168
|
eqtri |
|
170 |
163 169
|
eqtrdi |
|
171 |
|
xp2nd |
|
172 |
171
|
adantl |
|
173 |
|
fo2nd |
|
174 |
|
fof |
|
175 |
173 174
|
mp1i |
|
176 |
175
|
feqmptd |
|
177 |
176
|
reseq1d |
|
178 |
|
ssv |
|
179 |
|
resmpt |
|
180 |
178 179
|
ax-mp |
|
181 |
177 180
|
eqtrdi |
|
182 |
|
eqidd |
|
183 |
|
oveq2 |
|
184 |
172 181 182 183
|
fmptco |
|
185 |
161 170 184
|
3eqtr4a |
|
186 |
185
|
oveq2d |
|
187 |
151 186
|
eqtr4d |
|
188 |
116 187
|
chvarvv |
|
189 |
188
|
adantr |
|
190 |
189
|
oveq2d |
|
191 |
111 190
|
eqtrd |
|
192 |
96 191
|
eqeq12d |
|
193 |
48 192
|
syl5ibr |
|
194 |
193
|
expcom |
|
195 |
194
|
a2d |
|
196 |
25 32 39 46 47 195
|
findcard2s |
|
197 |
12 196
|
mpcom |
|