Step |
Hyp |
Ref |
Expression |
1 |
|
srgbinom.s |
|
2 |
|
srgbinom.m |
|
3 |
|
srgbinom.t |
|
4 |
|
srgbinom.a |
|
5 |
|
srgbinom.g |
|
6 |
|
srgbinom.e |
|
7 |
|
srgbinomlem.r |
|
8 |
|
srgbinomlem.a |
|
9 |
|
srgbinomlem.b |
|
10 |
|
srgbinomlem.c |
|
11 |
|
srgbinomlem.n |
|
12 |
|
srgbinomlem.i |
|
13 |
12
|
oveq1d |
|
14 |
|
eqid |
|
15 |
|
ovexd |
|
16 |
|
simpl |
|
17 |
|
elfzelz |
|
18 |
|
bccl |
|
19 |
11 17 18
|
syl2an |
|
20 |
|
fznn0sub |
|
21 |
20
|
adantl |
|
22 |
|
elfznn0 |
|
23 |
22
|
adantl |
|
24 |
1 2 3 4 5 6 7 8 9 10 11
|
srgbinomlem2 |
|
25 |
16 19 21 23 24
|
syl13anc |
|
26 |
|
eqid |
|
27 |
|
fzfid |
|
28 |
|
ovexd |
|
29 |
|
fvexd |
|
30 |
26 27 28 29
|
fsuppmptdm |
|
31 |
1 14 4 2 7 15 9 25 30
|
srgsummulcr |
|
32 |
|
srgcmn |
|
33 |
7 32
|
syl |
|
34 |
|
1z |
|
35 |
34
|
a1i |
|
36 |
|
0zd |
|
37 |
11
|
nn0zd |
|
38 |
7
|
adantr |
|
39 |
9
|
adantr |
|
40 |
1 2
|
srgcl |
|
41 |
38 25 39 40
|
syl3anc |
|
42 |
|
oveq2 |
|
43 |
|
oveq2 |
|
44 |
43
|
oveq1d |
|
45 |
|
oveq1 |
|
46 |
44 45
|
oveq12d |
|
47 |
42 46
|
oveq12d |
|
48 |
47
|
oveq1d |
|
49 |
1 14 33 35 36 37 41 48
|
gsummptshft |
|
50 |
11
|
nn0cnd |
|
51 |
50
|
adantr |
|
52 |
|
elfzelz |
|
53 |
52
|
adantl |
|
54 |
53
|
zcnd |
|
55 |
|
1cnd |
|
56 |
51 54 55
|
subsub3d |
|
57 |
56
|
oveq1d |
|
58 |
57
|
oveq1d |
|
59 |
58
|
oveq2d |
|
60 |
59
|
oveq1d |
|
61 |
7
|
adantr |
|
62 |
|
peano2zm |
|
63 |
52 62
|
syl |
|
64 |
|
bccl |
|
65 |
11 63 64
|
syl2an |
|
66 |
5 1
|
mgpbas |
|
67 |
5
|
srgmgp |
|
68 |
7 67
|
syl |
|
69 |
68
|
adantr |
|
70 |
|
0p1e1 |
|
71 |
70
|
oveq1i |
|
72 |
71
|
eleq2i |
|
73 |
|
fznn0sub |
|
74 |
73
|
a1i |
|
75 |
72 74
|
biimtrid |
|
76 |
75
|
imp |
|
77 |
8
|
adantr |
|
78 |
66 6 69 76 77
|
mulgnn0cld |
|
79 |
|
elfznn |
|
80 |
|
nnm1nn0 |
|
81 |
79 80
|
syl |
|
82 |
72 81
|
sylbi |
|
83 |
82
|
adantl |
|
84 |
9
|
adantr |
|
85 |
66 6 69 83 84
|
mulgnn0cld |
|
86 |
1 3 2
|
srgmulgass |
|
87 |
61 65 78 85 86
|
syl13anc |
|
88 |
87
|
eqcomd |
|
89 |
88
|
oveq1d |
|
90 |
|
srgmnd |
|
91 |
7 90
|
syl |
|
92 |
91
|
adantr |
|
93 |
1 3 92 65 78
|
mulgnn0cld |
|
94 |
1 2
|
srgass |
|
95 |
61 93 85 84 94
|
syl13anc |
|
96 |
5 2
|
mgpplusg |
|
97 |
66 6 96
|
mulgnn0p1 |
|
98 |
97
|
eqcomd |
|
99 |
69 83 84 98
|
syl3anc |
|
100 |
99
|
oveq2d |
|
101 |
52
|
zcnd |
|
102 |
|
1cnd |
|
103 |
101 102
|
npcand |
|
104 |
103
|
adantl |
|
105 |
104
|
oveq1d |
|
106 |
105
|
oveq2d |
|
107 |
95 100 106
|
3eqtrd |
|
108 |
60 89 107
|
3eqtrd |
|
109 |
108
|
mpteq2dva |
|
110 |
109
|
oveq2d |
|
111 |
71
|
mpteq1i |
|
112 |
|
oveq1 |
|
113 |
112
|
oveq2d |
|
114 |
|
oveq2 |
|
115 |
114
|
oveq1d |
|
116 |
113 115
|
oveq12d |
|
117 |
|
oveq1 |
|
118 |
116 117
|
oveq12d |
|
119 |
118
|
cbvmptv |
|
120 |
111 119
|
eqtri |
|
121 |
120
|
oveq2i |
|
122 |
|
fzfid |
|
123 |
|
simpl |
|
124 |
|
elfzelz |
|
125 |
|
peano2zm |
|
126 |
124 125
|
syl |
|
127 |
|
bccl |
|
128 |
11 126 127
|
syl2an |
|
129 |
|
fznn0sub |
|
130 |
129
|
adantl |
|
131 |
|
elfznn |
|
132 |
131
|
nnnn0d |
|
133 |
132
|
adantl |
|
134 |
1 2 3 4 5 6 7 8 9 10 11
|
srgbinomlem2 |
|
135 |
123 128 130 133 134
|
syl13anc |
|
136 |
135
|
ralrimiva |
|
137 |
1 33 122 136
|
gsummptcl |
|
138 |
1 4 14
|
mndlid |
|
139 |
91 137 138
|
syl2anc |
|
140 |
|
0nn0 |
|
141 |
140
|
a1i |
|
142 |
|
id |
|
143 |
|
0z |
|
144 |
143 34
|
pm3.2i |
|
145 |
|
zsubcl |
|
146 |
144 145
|
mp1i |
|
147 |
|
bccl |
|
148 |
11 146 147
|
syl2anc |
|
149 |
|
nn0cn |
|
150 |
|
peano2cn |
|
151 |
149 150
|
syl |
|
152 |
151
|
subid1d |
|
153 |
|
peano2nn0 |
|
154 |
152 153
|
eqeltrd |
|
155 |
11 154
|
syl |
|
156 |
1 2 3 4 5 6 7 8 9 10 11
|
srgbinomlem2 |
|
157 |
142 148 155 141 156
|
syl13anc |
|
158 |
|
oveq1 |
|
159 |
158
|
oveq2d |
|
160 |
|
oveq2 |
|
161 |
160
|
oveq1d |
|
162 |
|
oveq1 |
|
163 |
161 162
|
oveq12d |
|
164 |
159 163
|
oveq12d |
|
165 |
1 164
|
gsumsn |
|
166 |
91 141 157 165
|
syl3anc |
|
167 |
|
0lt1 |
|
168 |
167
|
a1i |
|
169 |
168 70
|
breqtrrdi |
|
170 |
|
0re |
|
171 |
|
1re |
|
172 |
170 171 170
|
3pm3.2i |
|
173 |
|
ltsubadd |
|
174 |
172 173
|
mp1i |
|
175 |
169 174
|
mpbird |
|
176 |
175
|
orcd |
|
177 |
|
bcval4 |
|
178 |
11 146 176 177
|
syl3anc |
|
179 |
178
|
oveq1d |
|
180 |
66 6 68 155 8
|
mulgnn0cld |
|
181 |
66 6 68 141 9
|
mulgnn0cld |
|
182 |
1 2
|
srgcl |
|
183 |
7 180 181 182
|
syl3anc |
|
184 |
1 14 3
|
mulg0 |
|
185 |
183 184
|
syl |
|
186 |
166 179 185
|
3eqtrrd |
|
187 |
186
|
oveq1d |
|
188 |
139 187
|
eqtr3d |
|
189 |
7
|
adantr |
|
190 |
68
|
adantr |
|
191 |
8
|
adantr |
|
192 |
66 6 190 130 191
|
mulgnn0cld |
|
193 |
9
|
adantr |
|
194 |
66 6 190 133 193
|
mulgnn0cld |
|
195 |
1 3 2
|
srgmulgass |
|
196 |
189 128 192 194 195
|
syl13anc |
|
197 |
196
|
mpteq2dva |
|
198 |
197
|
oveq2d |
|
199 |
11 153
|
syl |
|
200 |
|
simpl |
|
201 |
|
elfzelz |
|
202 |
201 125
|
syl |
|
203 |
11 202 127
|
syl2an |
|
204 |
|
fznn0sub |
|
205 |
204
|
adantl |
|
206 |
|
elfznn0 |
|
207 |
206
|
adantl |
|
208 |
200 203 205 207 134
|
syl13anc |
|
209 |
1 4 33 199 208
|
gsummptfzsplitl |
|
210 |
|
snfi |
|
211 |
210
|
a1i |
|
212 |
164
|
eleq1d |
|
213 |
212
|
ralsng |
|
214 |
140 213
|
ax-mp |
|
215 |
157 214
|
sylibr |
|
216 |
1 33 211 215
|
gsummptcl |
|
217 |
1 4
|
cmncom |
|
218 |
33 137 216 217
|
syl3anc |
|
219 |
209 218
|
eqtrd |
|
220 |
188 198 219
|
3eqtr4d |
|
221 |
121 220
|
eqtrid |
|
222 |
49 110 221
|
3eqtrd |
|
223 |
31 222
|
eqtr3d |
|
224 |
13 223
|
sylan9eqr |
|