Step |
Hyp |
Ref |
Expression |
1 |
|
esumcst.1 |
|
2 |
|
esumcst.2 |
|
3 |
1
|
nfel1 |
|
4 |
2
|
nfel1 |
|
5 |
3 4
|
nfan |
|
6 |
|
simpl |
|
7 |
|
simplr |
|
8 |
|
xrge0tmd |
|
9 |
|
tmdmnd |
|
10 |
8 9
|
ax-mp |
|
11 |
10
|
a1i |
|
12 |
|
inss2 |
|
13 |
|
simpr |
|
14 |
12 13
|
sseldi |
|
15 |
|
simplr |
|
16 |
|
xrge0base |
|
17 |
|
eqid |
|
18 |
2 16 17
|
gsumconstf |
|
19 |
11 14 15 18
|
syl3anc |
|
20 |
|
hashcl |
|
21 |
14 20
|
syl |
|
22 |
|
xrge0mulgnn0 |
|
23 |
21 15 22
|
syl2anc |
|
24 |
19 23
|
eqtrd |
|
25 |
5 1 6 7 24
|
esumval |
|
26 |
|
nn0ssre |
|
27 |
|
ressxr |
|
28 |
26 27
|
sstri |
|
29 |
|
pnfxr |
|
30 |
|
snssi |
|
31 |
29 30
|
ax-mp |
|
32 |
28 31
|
unssi |
|
33 |
|
hashf |
|
34 |
|
vex |
|
35 |
|
ffvelrn |
|
36 |
33 34 35
|
mp2an |
|
37 |
32 36
|
sselii |
|
38 |
37
|
a1i |
|
39 |
|
iccssxr |
|
40 |
|
simpr |
|
41 |
39 40
|
sseldi |
|
42 |
41
|
adantr |
|
43 |
38 42
|
xmulcld |
|
44 |
43
|
fmpttd |
|
45 |
44
|
frnd |
|
46 |
|
hashxrcl |
|
47 |
46
|
adantr |
|
48 |
47 41
|
xmulcld |
|
49 |
|
vex |
|
50 |
|
eqid |
|
51 |
50
|
elrnmpt |
|
52 |
49 51
|
ax-mp |
|
53 |
52
|
biimpi |
|
54 |
47
|
adantr |
|
55 |
|
0xr |
|
56 |
55
|
a1i |
|
57 |
29
|
a1i |
|
58 |
|
iccgelb |
|
59 |
56 57 15 58
|
syl3anc |
|
60 |
42 59
|
jca |
|
61 |
6
|
adantr |
|
62 |
|
inss1 |
|
63 |
62
|
sseli |
|
64 |
|
elpwi |
|
65 |
13 63 64
|
3syl |
|
66 |
|
ssdomg |
|
67 |
61 65 66
|
sylc |
|
68 |
|
hashdomi |
|
69 |
67 68
|
syl |
|
70 |
|
xlemul1a |
|
71 |
38 54 60 69 70
|
syl31anc |
|
72 |
71
|
ralrimiva |
|
73 |
|
r19.29r |
|
74 |
53 72 73
|
syl2anr |
|
75 |
|
simpl |
|
76 |
|
simpr |
|
77 |
75 76
|
eqbrtrd |
|
78 |
77
|
rexlimivw |
|
79 |
74 78
|
syl |
|
80 |
79
|
ralrimiva |
|
81 |
|
pwidg |
|
82 |
81
|
ancri |
|
83 |
|
elin |
|
84 |
82 83
|
sylibr |
|
85 |
|
eqid |
|
86 |
|
fveq2 |
|
87 |
86
|
oveq1d |
|
88 |
87
|
rspceeqv |
|
89 |
85 88
|
mpan2 |
|
90 |
|
ovex |
|
91 |
50
|
elrnmpt |
|
92 |
90 91
|
ax-mp |
|
93 |
89 92
|
sylibr |
|
94 |
84 93
|
syl |
|
95 |
94
|
adantl |
|
96 |
|
simplr |
|
97 |
|
breq2 |
|
98 |
97
|
rspcev |
|
99 |
95 96 98
|
syl2anc |
|
100 |
|
0elpw |
|
101 |
|
0fin |
|
102 |
|
elin |
|
103 |
100 101 102
|
mpbir2an |
|
104 |
103
|
a1i |
|
105 |
|
simpr |
|
106 |
105
|
oveq2d |
|
107 |
|
hash0 |
|
108 |
107 55
|
eqeltri |
|
109 |
|
xmul01 |
|
110 |
108 109
|
ax-mp |
|
111 |
106 110
|
eqtr2di |
|
112 |
|
fveq2 |
|
113 |
112
|
oveq1d |
|
114 |
113
|
rspceeqv |
|
115 |
104 111 114
|
syl2anc |
|
116 |
|
ovex |
|
117 |
50 116
|
elrnmpti |
|
118 |
115 117
|
sylibr |
|
119 |
|
simpllr |
|
120 |
105
|
oveq2d |
|
121 |
47
|
ad4antr |
|
122 |
|
xmul01 |
|
123 |
121 122
|
syl |
|
124 |
120 123
|
eqtrd |
|
125 |
119 124
|
breqtrd |
|
126 |
|
breq2 |
|
127 |
126
|
rspcev |
|
128 |
118 125 127
|
syl2anc |
|
129 |
|
simplr |
|
130 |
|
simpr |
|
131 |
|
simp-4r |
|
132 |
130 131
|
eqeltrd |
|
133 |
|
nnnn0 |
|
134 |
|
vex |
|
135 |
|
hashclb |
|
136 |
134 135
|
ax-mp |
|
137 |
133 136
|
sylibr |
|
138 |
132 137
|
syl |
|
139 |
129 138
|
elind |
|
140 |
|
eqidd |
|
141 |
|
fveq2 |
|
142 |
141
|
oveq1d |
|
143 |
142
|
rspceeqv |
|
144 |
139 140 143
|
syl2anc |
|
145 |
50 116
|
elrnmpti |
|
146 |
144 145
|
sylibr |
|
147 |
|
simpllr |
|
148 |
|
simp-8r |
|
149 |
131
|
nnred |
|
150 |
|
simp-5r |
|
151 |
148 149 150
|
ltdivmul2d |
|
152 |
147 151
|
mpbid |
|
153 |
130
|
oveq1d |
|
154 |
150
|
rpred |
|
155 |
|
rexmul |
|
156 |
149 154 155
|
syl2anc |
|
157 |
153 156
|
eqtrd |
|
158 |
152 157
|
breqtrrd |
|
159 |
|
breq2 |
|
160 |
159
|
rspcev |
|
161 |
146 158 160
|
syl2anc |
|
162 |
161
|
rexlimdva2 |
|
163 |
162
|
impr |
|
164 |
|
simp-4r |
|
165 |
|
simpr |
|
166 |
164 165
|
rerpdivcld |
|
167 |
|
arch |
|
168 |
166 167
|
syl |
|
169 |
|
ishashinf |
|
170 |
169
|
ad2antlr |
|
171 |
|
r19.29r |
|
172 |
168 170 171
|
syl2anc |
|
173 |
163 172
|
r19.29a |
|
174 |
|
nfielex |
|
175 |
174
|
adantr |
|
176 |
|
snelpwi |
|
177 |
|
snfi |
|
178 |
176 177
|
jctir |
|
179 |
|
elin |
|
180 |
178 179
|
sylibr |
|
181 |
180
|
adantl |
|
182 |
|
simplr |
|
183 |
182
|
oveq2d |
|
184 |
|
hashsng |
|
185 |
|
1re |
|
186 |
27 185
|
sselii |
|
187 |
184 186
|
eqeltrdi |
|
188 |
|
0lt1 |
|
189 |
188 184
|
breqtrrid |
|
190 |
|
xmulpnf1 |
|
191 |
187 189 190
|
syl2anc |
|
192 |
191
|
adantl |
|
193 |
183 192
|
eqtr2d |
|
194 |
|
fveq2 |
|
195 |
194
|
oveq1d |
|
196 |
195
|
rspceeqv |
|
197 |
181 193 196
|
syl2anc |
|
198 |
175 197
|
exlimddv |
|
199 |
198
|
adantll |
|
200 |
50 116
|
elrnmpti |
|
201 |
199 200
|
sylibr |
|
202 |
|
simp-4r |
|
203 |
|
ltpnf |
|
204 |
202 203
|
syl |
|
205 |
|
breq2 |
|
206 |
205
|
rspcev |
|
207 |
201 204 206
|
syl2anc |
|
208 |
|
simp-4r |
|
209 |
|
elxrge02 |
|
210 |
208 209
|
sylib |
|
211 |
128 173 207 210
|
mpjao3dan |
|
212 |
99 211
|
pm2.61dan |
|
213 |
212
|
ex |
|
214 |
213
|
ralrimiva |
|
215 |
|
supxr2 |
|
216 |
45 48 80 214 215
|
syl22anc |
|
217 |
25 216
|
eqtrd |
|