Step |
Hyp |
Ref |
Expression |
1 |
|
fzsum2sub.m |
|
2 |
|
fzsum2sub.n |
|
3 |
|
fzsum2sub.1 |
|
4 |
|
fzsum2sub.2 |
|
5 |
|
fzsum2sub.3 |
|
6 |
|
fzsum2sub.4 |
|
7 |
|
simpr |
|
8 |
7
|
elfzelzd |
|
9 |
|
0zd |
|
10 |
1
|
nn0zd |
|
11 |
10
|
adantr |
|
12 |
|
simpll |
|
13 |
|
fz1ssnn |
|
14 |
|
nnssnn0 |
|
15 |
13 14
|
sstri |
|
16 |
15 7
|
sseldi |
|
17 |
|
nn0uz |
|
18 |
16 17
|
eleqtrdi |
|
19 |
|
neg0 |
|
20 |
|
uzneg |
|
21 |
19 20
|
eqeltrrid |
|
22 |
|
fzss1 |
|
23 |
18 21 22
|
3syl |
|
24 |
|
fzssuz |
|
25 |
23 24
|
sstrdi |
|
26 |
25
|
sselda |
|
27 |
7
|
adantr |
|
28 |
12 26 27 4
|
syl3anc |
|
29 |
8 9 11 28 3
|
fsumshft |
|
30 |
1
|
adantr |
|
31 |
13 7
|
sseldi |
|
32 |
31
|
nnnn0d |
|
33 |
30 32
|
nn0addcld |
|
34 |
33
|
nn0red |
|
35 |
34
|
ltp1d |
|
36 |
|
fzdisj |
|
37 |
35 36
|
syl |
|
38 |
2
|
nn0zd |
|
39 |
10 38
|
zaddcld |
|
40 |
39
|
adantr |
|
41 |
33
|
nn0zd |
|
42 |
31
|
nnred |
|
43 |
|
nn0addge2 |
|
44 |
42 30 43
|
syl2anc |
|
45 |
2
|
nn0red |
|
46 |
45
|
adantr |
|
47 |
30
|
nn0red |
|
48 |
|
elfzle2 |
|
49 |
48
|
adantl |
|
50 |
42 46 47 49
|
leadd2dd |
|
51 |
8 40 41 44 50
|
elfzd |
|
52 |
|
fzsplit |
|
53 |
51 52
|
syl |
|
54 |
|
fzfid |
|
55 |
|
simpll |
|
56 |
7
|
adantr |
|
57 |
15 56
|
sseldi |
|
58 |
|
fz2ssnn0 |
|
59 |
57 58
|
syl |
|
60 |
|
simpr |
|
61 |
59 60
|
sseldd |
|
62 |
3
|
eleq1d |
|
63 |
|
simpll |
|
64 |
|
simplr |
|
65 |
|
simpr |
|
66 |
63 64 65 4
|
syl3anc |
|
67 |
66
|
an32s |
|
68 |
67
|
ralrimiva |
|
69 |
68
|
adantr |
|
70 |
|
nnsscn |
|
71 |
13 70
|
sstri |
|
72 |
|
simplr |
|
73 |
71 72
|
sseldi |
|
74 |
|
simpr |
|
75 |
74
|
nn0cnd |
|
76 |
73 75
|
negsubdi2d |
|
77 |
72
|
elfzelzd |
|
78 |
|
eluzmn |
|
79 |
77 74 78
|
syl2anc |
|
80 |
|
uzneg |
|
81 |
79 80
|
syl |
|
82 |
76 81
|
eqeltrrd |
|
83 |
62 69 82
|
rspcdva |
|
84 |
55 56 61 83
|
syl21anc |
|
85 |
37 53 54 84
|
fsumsplit |
|
86 |
8
|
zcnd |
|
87 |
86
|
addid2d |
|
88 |
87
|
oveq1d |
|
89 |
88
|
eqcomd |
|
90 |
89
|
sumeq1d |
|
91 |
5
|
sumeq2dv |
|
92 |
|
fzfi |
|
93 |
|
sumz |
|
94 |
93
|
olcs |
|
95 |
92 94
|
ax-mp |
|
96 |
91 95
|
eqtrdi |
|
97 |
90 96
|
oveq12d |
|
98 |
|
fzfid |
|
99 |
|
simpll |
|
100 |
7
|
adantr |
|
101 |
|
elfzuz3 |
|
102 |
101
|
adantl |
|
103 |
|
eluzadd |
|
104 |
102 11 103
|
syl2anc |
|
105 |
2
|
nn0cnd |
|
106 |
105
|
adantr |
|
107 |
|
zsscn |
|
108 |
107 11
|
sseldi |
|
109 |
106 108
|
addcomd |
|
110 |
86 108
|
addcomd |
|
111 |
110
|
fveq2d |
|
112 |
104 109 111
|
3eltr3d |
|
113 |
112
|
adantr |
|
114 |
|
fzss2 |
|
115 |
113 114
|
syl |
|
116 |
|
simpr |
|
117 |
88
|
adantr |
|
118 |
116 117
|
eleqtrd |
|
119 |
115 118
|
sseldd |
|
120 |
99 100 119 61
|
syl21anc |
|
121 |
99 100 120 83
|
syl21anc |
|
122 |
98 121
|
fsumcl |
|
123 |
122
|
addid1d |
|
124 |
85 97 123
|
3eqtrrd |
|
125 |
|
fzval3 |
|
126 |
40 125
|
syl |
|
127 |
126
|
ineq2d |
|
128 |
|
fzodisj |
|
129 |
127 128
|
eqtrdi |
|
130 |
40
|
peano2zd |
|
131 |
32
|
nn0ge0d |
|
132 |
130
|
zred |
|
133 |
40
|
zred |
|
134 |
|
nn0addge2 |
|
135 |
45 1 134
|
syl2anc |
|
136 |
135
|
adantr |
|
137 |
133
|
lep1d |
|
138 |
46 133 132 136 137
|
letrd |
|
139 |
42 46 132 49 138
|
letrd |
|
140 |
9 130 8 131 139
|
elfzd |
|
141 |
|
fzosplit |
|
142 |
140 141
|
syl |
|
143 |
|
fzval3 |
|
144 |
40 143
|
syl |
|
145 |
126
|
uneq2d |
|
146 |
142 144 145
|
3eqtr4d |
|
147 |
|
fzfid |
|
148 |
147
|
adantr |
|
149 |
|
simpl |
|
150 |
7
|
adantrl |
|
151 |
|
fz0ssnn0 |
|
152 |
|
simprl |
|
153 |
151 152
|
sseldi |
|
154 |
149 150 153 83
|
syl21anc |
|
155 |
154
|
anass1rs |
|
156 |
129 146 148 155
|
fsumsplit |
|
157 |
6
|
sumeq2dv |
|
158 |
|
fzofi |
|
159 |
|
sumz |
|
160 |
159
|
olcs |
|
161 |
158 160
|
ax-mp |
|
162 |
157 161
|
eqtrdi |
|
163 |
162
|
oveq1d |
|
164 |
54 84
|
fsumcl |
|
165 |
164
|
addid2d |
|
166 |
156 163 165
|
3eqtrrd |
|
167 |
124 166
|
eqtrd |
|
168 |
29 167
|
eqtrd |
|
169 |
168
|
sumeq2dv |
|
170 |
|
fzfid |
|
171 |
|
fzfid |
|
172 |
28
|
anasss |
|
173 |
172
|
ancom2s |
|
174 |
170 171 173
|
fsumcom |
|
175 |
147 171 154
|
fsumcom |
|
176 |
169 174 175
|
3eqtr4d |
|