Step |
Hyp |
Ref |
Expression |
1 |
|
eulerpart.p |
|
2 |
|
eulerpart.o |
|
3 |
|
eulerpart.d |
|
4 |
|
eulerpart.j |
|
5 |
|
eulerpart.f |
|
6 |
|
eulerpart.h |
|
7 |
|
eulerpart.m |
|
8 |
|
eulerpart.r |
|
9 |
|
eulerpart.t |
|
10 |
|
eulerpart.g |
|
11 |
|
eulerpart.s |
|
12 |
|
cnvimass |
|
13 |
1 2 3 4 5 6 7 8 9 10
|
eulerpartgbij |
|
14 |
|
f1of |
|
15 |
13 14
|
ax-mp |
|
16 |
15
|
ffvelrni |
|
17 |
|
elin |
|
18 |
16 17
|
sylib |
|
19 |
18
|
simpld |
|
20 |
|
elmapi |
|
21 |
|
fdm |
|
22 |
19 20 21
|
3syl |
|
23 |
12 22
|
sseqtrid |
|
24 |
23
|
sselda |
|
25 |
1 2 3 4 5 6 7 8 9 10
|
eulerpartlemgvv |
|
26 |
25
|
oveq1d |
|
27 |
24 26
|
syldan |
|
28 |
27
|
sumeq2dv |
|
29 |
|
eqeq2 |
|
30 |
29
|
2rexbidv |
|
31 |
30
|
elrab |
|
32 |
31
|
simprbi |
|
33 |
32
|
iftrued |
|
34 |
33
|
oveq1d |
|
35 |
|
elrabi |
|
36 |
35
|
nncnd |
|
37 |
36
|
mulid2d |
|
38 |
34 37
|
eqtrd |
|
39 |
38
|
sumeq2i |
|
40 |
|
id |
|
41 |
1 2 3 4 5 6 7 8 9 10
|
eulerpartlemgf |
|
42 |
35
|
adantl |
|
43 |
42 25
|
syldan |
|
44 |
32
|
adantl |
|
45 |
44
|
iftrued |
|
46 |
43 45
|
eqtrd |
|
47 |
|
1nn |
|
48 |
46 47
|
eqeltrdi |
|
49 |
19 20
|
syl |
|
50 |
|
ffn |
|
51 |
|
elpreima |
|
52 |
49 50 51
|
3syl |
|
53 |
52
|
adantr |
|
54 |
42 48 53
|
mpbir2and |
|
55 |
54
|
ex |
|
56 |
55
|
ssrdv |
|
57 |
|
ssfi |
|
58 |
41 56 57
|
syl2anc |
|
59 |
|
cnvexg |
|
60 |
|
imaexg |
|
61 |
|
inex1g |
|
62 |
59 60 61
|
3syl |
|
63 |
|
snex |
|
64 |
|
fvex |
|
65 |
63 64
|
xpex |
|
66 |
65
|
rgenw |
|
67 |
|
iunexg |
|
68 |
62 66 67
|
sylancl |
|
69 |
|
eqid |
|
70 |
1 2 3 4 5 6 7 8 9 10 69
|
eulerpartlemgh |
|
71 |
|
f1oeng |
|
72 |
68 70 71
|
syl2anc |
|
73 |
|
enfii |
|
74 |
58 72 73
|
syl2anc |
|
75 |
|
fvres |
|
76 |
75
|
adantl |
|
77 |
|
inss2 |
|
78 |
|
simpr |
|
79 |
77 78
|
sseldi |
|
80 |
79
|
snssd |
|
81 |
|
bitsss |
|
82 |
|
xpss12 |
|
83 |
80 81 82
|
sylancl |
|
84 |
83
|
ralrimiva |
|
85 |
|
iunss |
|
86 |
84 85
|
sylibr |
|
87 |
86
|
sselda |
|
88 |
4 5
|
oddpwdcv |
|
89 |
87 88
|
syl |
|
90 |
76 89
|
eqtrd |
|
91 |
42
|
nncnd |
|
92 |
40 74 70 90 91
|
fsumf1o |
|
93 |
39 92
|
syl5eq |
|
94 |
|
ax-1cn |
|
95 |
|
0cn |
|
96 |
94 95
|
ifcli |
|
97 |
96
|
a1i |
|
98 |
|
ssrab2 |
|
99 |
|
simpr |
|
100 |
98 99
|
sseldi |
|
101 |
100
|
nncnd |
|
102 |
97 101
|
mulcld |
|
103 |
|
simpr |
|
104 |
103
|
eldifbd |
|
105 |
23
|
ssdifssd |
|
106 |
105
|
sselda |
|
107 |
31
|
notbii |
|
108 |
|
imnan |
|
109 |
107 108
|
sylbb2 |
|
110 |
104 106 109
|
sylc |
|
111 |
110
|
iffalsed |
|
112 |
111
|
oveq1d |
|
113 |
|
nnsscn |
|
114 |
105 113
|
sstrdi |
|
115 |
114
|
sselda |
|
116 |
115
|
mul02d |
|
117 |
112 116
|
eqtrd |
|
118 |
56 102 117 41
|
fsumss |
|
119 |
93 118
|
eqtr3d |
|
120 |
1 2 3 4 5 6 7 8 9
|
eulerpartlemt0 |
|
121 |
120
|
simp1bi |
|
122 |
|
elmapi |
|
123 |
121 122
|
syl |
|
124 |
123
|
adantr |
|
125 |
|
cnvimass |
|
126 |
125 123
|
fssdm |
|
127 |
126
|
adantr |
|
128 |
|
inss1 |
|
129 |
128 78
|
sseldi |
|
130 |
127 129
|
sseldd |
|
131 |
124 130
|
ffvelrnd |
|
132 |
|
bitsfi |
|
133 |
131 132
|
syl |
|
134 |
130
|
nncnd |
|
135 |
|
2cnd |
|
136 |
|
simprr |
|
137 |
81 136
|
sseldi |
|
138 |
135 137
|
expcld |
|
139 |
138
|
anassrs |
|
140 |
133 134 139
|
fsummulc1 |
|
141 |
140
|
sumeq2dv |
|
142 |
|
bitsinv1 |
|
143 |
142
|
oveq1d |
|
144 |
131 143
|
syl |
|
145 |
144
|
sumeq2dv |
|
146 |
|
vex |
|
147 |
|
vex |
|
148 |
146 147
|
op2ndd |
|
149 |
148
|
oveq2d |
|
150 |
146 147
|
op1std |
|
151 |
149 150
|
oveq12d |
|
152 |
|
inss2 |
|
153 |
152
|
sseli |
|
154 |
|
cnveq |
|
155 |
154
|
imaeq1d |
|
156 |
155
|
eleq1d |
|
157 |
156 8
|
elab2g |
|
158 |
153 157
|
mpbid |
|
159 |
|
ssfi |
|
160 |
158 128 159
|
sylancl |
|
161 |
134
|
adantrr |
|
162 |
138 161
|
mulcld |
|
163 |
151 160 133 162
|
fsum2d |
|
164 |
141 145 163
|
3eqtr3d |
|
165 |
|
inss1 |
|
166 |
165
|
sseli |
|
167 |
155
|
sseq1d |
|
168 |
167 9
|
elrab2 |
|
169 |
168
|
simprbi |
|
170 |
166 169
|
syl |
|
171 |
|
df-ss |
|
172 |
170 171
|
sylib |
|
173 |
172
|
sumeq1d |
|
174 |
164 173
|
eqtr3d |
|
175 |
28 119 174
|
3eqtr2d |
|
176 |
|
fveq2 |
|
177 |
|
id |
|
178 |
176 177
|
oveq12d |
|
179 |
178
|
cbvsumv |
|
180 |
175 179
|
eqtr4di |
|
181 |
|
0nn0 |
|
182 |
|
1nn0 |
|
183 |
|
prssi |
|
184 |
181 182 183
|
mp2an |
|
185 |
|
fss |
|
186 |
184 185
|
mpan2 |
|
187 |
|
nn0ex |
|
188 |
|
nnex |
|
189 |
187 188
|
elmap |
|
190 |
189
|
biimpri |
|
191 |
20 186 190
|
3syl |
|
192 |
191
|
anim1i |
|
193 |
|
elin |
|
194 |
192 17 193
|
3imtr4i |
|
195 |
8 11
|
eulerpartlemsv2 |
|
196 |
16 194 195
|
3syl |
|
197 |
121 153
|
elind |
|
198 |
8 11
|
eulerpartlemsv2 |
|
199 |
197 198
|
syl |
|
200 |
180 196 199
|
3eqtr4d |
|