Step |
Hyp |
Ref |
Expression |
1 |
|
oveq2 |
|
2 |
1
|
sumeq1d |
|
3 |
1
|
sumeq1d |
|
4 |
3
|
oveq2d |
|
5 |
4
|
sumeq1d |
|
6 |
2 5
|
eqeq12d |
|
7 |
|
oveq2 |
|
8 |
7
|
sumeq1d |
|
9 |
7
|
sumeq1d |
|
10 |
9
|
oveq2d |
|
11 |
10
|
sumeq1d |
|
12 |
8 11
|
eqeq12d |
|
13 |
|
oveq2 |
|
14 |
13
|
sumeq1d |
|
15 |
13
|
sumeq1d |
|
16 |
15
|
oveq2d |
|
17 |
16
|
sumeq1d |
|
18 |
14 17
|
eqeq12d |
|
19 |
|
oveq2 |
|
20 |
19
|
sumeq1d |
|
21 |
19
|
sumeq1d |
|
22 |
21
|
oveq2d |
|
23 |
22
|
sumeq1d |
|
24 |
20 23
|
eqeq12d |
|
25 |
|
sum0 |
|
26 |
|
sum0 |
|
27 |
25 26
|
eqtr4i |
|
28 |
|
fz10 |
|
29 |
28
|
sumeq1i |
|
30 |
28
|
sumeq1i |
|
31 |
|
sum0 |
|
32 |
30 31
|
eqtri |
|
33 |
32
|
oveq2i |
|
34 |
33 28
|
eqtri |
|
35 |
34
|
sumeq1i |
|
36 |
27 29 35
|
3eqtr4i |
|
37 |
|
simpr |
|
38 |
|
fzfid |
|
39 |
|
elfznn |
|
40 |
39
|
adantl |
|
41 |
40
|
nnnn0d |
|
42 |
38 41
|
fsumnn0cl |
|
43 |
42
|
nn0zd |
|
44 |
|
nn0p1nn |
|
45 |
42 44
|
syl |
|
46 |
45
|
nnzd |
|
47 |
|
peano2nn0 |
|
48 |
47
|
nn0zd |
|
49 |
43 48
|
zaddcld |
|
50 |
|
2cnd |
|
51 |
|
elfzelz |
|
52 |
51
|
zcnd |
|
53 |
52
|
adantl |
|
54 |
50 53
|
mulcld |
|
55 |
|
1cnd |
|
56 |
54 55
|
subcld |
|
57 |
|
oveq2 |
|
58 |
57
|
oveq1d |
|
59 |
43 46 49 56 58
|
fsumshftm |
|
60 |
|
elfzelz |
|
61 |
60
|
adantl |
|
62 |
61
|
zred |
|
63 |
38 62
|
fsumrecl |
|
64 |
63
|
recnd |
|
65 |
|
1cnd |
|
66 |
64 65
|
pncan2d |
|
67 |
47
|
nn0cnd |
|
68 |
64 67
|
pncan2d |
|
69 |
66 68
|
oveq12d |
|
70 |
|
elfzelz |
|
71 |
70
|
zcnd |
|
72 |
|
2cnd |
|
73 |
|
simpr |
|
74 |
64
|
adantr |
|
75 |
72 73 74
|
adddid |
|
76 |
75
|
oveq1d |
|
77 |
72 73
|
mulcld |
|
78 |
72 74
|
mulcld |
|
79 |
|
1cnd |
|
80 |
77 78 79
|
addsubassd |
|
81 |
77 78 79
|
addsub12d |
|
82 |
|
arisum |
|
83 |
82
|
oveq2d |
|
84 |
|
nn0cn |
|
85 |
84
|
sqcld |
|
86 |
85 84
|
addcld |
|
87 |
|
2cnd |
|
88 |
|
2ne0 |
|
89 |
88
|
a1i |
|
90 |
86 87 89
|
divcan2d |
|
91 |
|
binom21 |
|
92 |
84 91
|
syl |
|
93 |
92
|
oveq1d |
|
94 |
87 84
|
mulcld |
|
95 |
85 94
|
addcld |
|
96 |
95 84 65
|
pnpcan2d |
|
97 |
85 94 84
|
addsubassd |
|
98 |
84
|
2timesd |
|
99 |
84 84 98
|
mvrladdd |
|
100 |
99
|
oveq2d |
|
101 |
97 100
|
eqtrd |
|
102 |
93 96 101
|
3eqtrrd |
|
103 |
83 90 102
|
3eqtrd |
|
104 |
103
|
adantr |
|
105 |
104
|
oveq1d |
|
106 |
81 105
|
eqtrd |
|
107 |
76 80 106
|
3eqtrd |
|
108 |
71 107
|
sylan2 |
|
109 |
69 108
|
sumeq12dv |
|
110 |
59 109
|
eqtr2d |
|
111 |
110
|
adantr |
|
112 |
37 111
|
oveq12d |
|
113 |
|
id |
|
114 |
|
fzfid |
|
115 |
|
elfzelz |
|
116 |
115
|
zcnd |
|
117 |
116
|
sqcld |
|
118 |
117 116
|
subcld |
|
119 |
|
2cnd |
|
120 |
|
elfzelz |
|
121 |
120
|
zcnd |
|
122 |
119 121
|
mulcld |
|
123 |
|
1cnd |
|
124 |
122 123
|
subcld |
|
125 |
|
addcl |
|
126 |
118 124 125
|
syl2an |
|
127 |
126
|
adantll |
|
128 |
114 127
|
fsumcl |
|
129 |
|
oveq2 |
|
130 |
|
oveq1 |
|
131 |
|
id |
|
132 |
130 131
|
oveq12d |
|
133 |
132
|
oveq1d |
|
134 |
133
|
adantr |
|
135 |
129 134
|
sumeq12dv |
|
136 |
113 128 135
|
fz1sump1 |
|
137 |
136
|
adantr |
|
138 |
116
|
adantl |
|
139 |
113 138 131
|
fz1sump1 |
|
140 |
139
|
adantr |
|
141 |
140
|
oveq2d |
|
142 |
141
|
sumeq1d |
|
143 |
63
|
ltp1d |
|
144 |
|
fzdisj |
|
145 |
143 144
|
syl |
|
146 |
|
nnuz |
|
147 |
45 146
|
eleqtrdi |
|
148 |
43
|
uzidd |
|
149 |
|
uzaddcl |
|
150 |
148 47 149
|
syl2anc |
|
151 |
|
fzsplit2 |
|
152 |
147 150 151
|
syl2anc |
|
153 |
|
fzfid |
|
154 |
|
2cnd |
|
155 |
|
elfzelz |
|
156 |
155
|
zcnd |
|
157 |
156
|
adantl |
|
158 |
154 157
|
mulcld |
|
159 |
|
1cnd |
|
160 |
158 159
|
subcld |
|
161 |
145 152 153 160
|
fsumsplit |
|
162 |
161
|
adantr |
|
163 |
142 162
|
eqtrd |
|
164 |
112 137 163
|
3eqtr4d |
|
165 |
164
|
ex |
|
166 |
6 12 18 24 36 165
|
nn0ind |
|
167 |
|
fz1ssnn |
|
168 |
|
nnssnn0 |
|
169 |
167 168
|
sstri |
|
170 |
169
|
a1i |
|
171 |
170
|
sselda |
|
172 |
|
nicomachus |
|
173 |
171 172
|
syl |
|
174 |
173
|
sumeq2dv |
|
175 |
|
fzfid |
|
176 |
175 171
|
fsumnn0cl |
|
177 |
|
oddnumth |
|
178 |
176 177
|
syl |
|
179 |
166 174 178
|
3eqtr3d |
|