Step |
Hyp |
Ref |
Expression |
1 |
|
breprexp.n |
|
2 |
|
breprexp.s |
|
3 |
|
breprexplema.m |
|
4 |
|
breprexplema.1 |
|
5 |
|
breprexplema.l |
|
6 |
|
fz1ssnn |
|
7 |
6
|
a1i |
|
8 |
3
|
nn0zd |
|
9 |
|
eqid |
|
10 |
7 8 2 9
|
reprsuc |
|
11 |
10
|
sumeq1d |
|
12 |
|
fzfid |
|
13 |
6
|
a1i |
|
14 |
8
|
adantr |
|
15 |
|
fzssz |
|
16 |
|
simpr |
|
17 |
15 16
|
sseldi |
|
18 |
14 17
|
zsubcld |
|
19 |
2
|
adantr |
|
20 |
12
|
adantr |
|
21 |
13 18 19 20
|
reprfi |
|
22 |
|
mptfi |
|
23 |
21 22
|
syl |
|
24 |
|
rnfi |
|
25 |
23 24
|
syl |
|
26 |
13 18 19
|
reprval |
|
27 |
|
ssrab2 |
|
28 |
26 27
|
eqsstrdi |
|
29 |
12
|
elexd |
|
30 |
|
fzonel |
|
31 |
30
|
a1i |
|
32 |
28 29 2 31 9
|
actfunsnrndisj |
|
33 |
|
fzofi |
|
34 |
33
|
a1i |
|
35 |
5
|
ralrimiva |
|
36 |
35
|
ralrimiva |
|
37 |
36
|
ad3antrrr |
|
38 |
|
simpr |
|
39 |
|
nfv |
|
40 |
|
nfcv |
|
41 |
|
nfmpt1 |
|
42 |
41
|
nfrn |
|
43 |
40 42
|
nfel |
|
44 |
39 43
|
nfan |
|
45 |
6
|
a1i |
|
46 |
18
|
ad3antrrr |
|
47 |
19
|
ad3antrrr |
|
48 |
|
simplr |
|
49 |
45 46 47 48
|
reprf |
|
50 |
16
|
ad3antrrr |
|
51 |
47 50
|
fsnd |
|
52 |
|
fzodisjsn |
|
53 |
52
|
a1i |
|
54 |
|
fun2 |
|
55 |
49 51 53 54
|
syl21anc |
|
56 |
|
simpr |
|
57 |
|
nn0uz |
|
58 |
2 57
|
eleqtrdi |
|
59 |
|
fzosplitsn |
|
60 |
58 59
|
syl |
|
61 |
60
|
ad4antr |
|
62 |
56 61
|
feq12d |
|
63 |
55 62
|
mpbird |
|
64 |
|
simpr |
|
65 |
|
vex |
|
66 |
|
snex |
|
67 |
65 66
|
unex |
|
68 |
9 67
|
elrnmpti |
|
69 |
64 68
|
sylib |
|
70 |
44 63 69
|
r19.29af |
|
71 |
70
|
adantr |
|
72 |
71 38
|
ffvelrnd |
|
73 |
6 72
|
sseldi |
|
74 |
|
fveq2 |
|
75 |
74
|
fveq1d |
|
76 |
75
|
eleq1d |
|
77 |
|
fveq2 |
|
78 |
77
|
eleq1d |
|
79 |
76 78
|
rspc2v |
|
80 |
38 73 79
|
syl2anc |
|
81 |
37 80
|
mpd |
|
82 |
34 81
|
fprodcl |
|
83 |
82
|
anasss |
|
84 |
12 25 32 83
|
fsumiun |
|
85 |
60
|
ad2antrr |
|
86 |
85
|
prodeq1d |
|
87 |
|
nfv |
|
88 |
|
nfcv |
|
89 |
|
fzofi |
|
90 |
89
|
a1i |
|
91 |
19
|
adantr |
|
92 |
30
|
a1i |
|
93 |
6
|
a1i |
|
94 |
18
|
adantr |
|
95 |
|
simpr |
|
96 |
93 94 91 95
|
reprf |
|
97 |
96
|
ffnd |
|
98 |
97
|
adantr |
|
99 |
16
|
adantr |
|
100 |
|
fnsng |
|
101 |
91 99 100
|
syl2anc |
|
102 |
101
|
adantr |
|
103 |
52
|
a1i |
|
104 |
|
simpr |
|
105 |
|
fvun1 |
|
106 |
98 102 103 104 105
|
syl112anc |
|
107 |
106
|
fveq2d |
|
108 |
36
|
ad2antrr |
|
109 |
108
|
adantr |
|
110 |
|
fzossfzop1 |
|
111 |
2 110
|
syl |
|
112 |
111
|
ad2antrr |
|
113 |
112
|
sselda |
|
114 |
96
|
ffvelrnda |
|
115 |
6 114
|
sseldi |
|
116 |
|
fveq2 |
|
117 |
116
|
eleq1d |
|
118 |
76 117
|
rspc2v |
|
119 |
113 115 118
|
syl2anc |
|
120 |
109 119
|
mpd |
|
121 |
107 120
|
eqeltrd |
|
122 |
|
fveq2 |
|
123 |
|
fveq2 |
|
124 |
122 123
|
fveq12d |
|
125 |
52
|
a1i |
|
126 |
|
snidg |
|
127 |
91 126
|
syl |
|
128 |
|
fvun2 |
|
129 |
97 101 125 127 128
|
syl112anc |
|
130 |
|
fvsng |
|
131 |
91 99 130
|
syl2anc |
|
132 |
129 131
|
eqtrd |
|
133 |
132
|
fveq2d |
|
134 |
|
fzonn0p1 |
|
135 |
2 134
|
syl |
|
136 |
135
|
ad2antrr |
|
137 |
6 99
|
sseldi |
|
138 |
|
fveq2 |
|
139 |
138
|
fveq1d |
|
140 |
139
|
eleq1d |
|
141 |
|
fveq2 |
|
142 |
141
|
eleq1d |
|
143 |
140 142
|
rspc2v |
|
144 |
136 137 143
|
syl2anc |
|
145 |
108 144
|
mpd |
|
146 |
133 145
|
eqeltrd |
|
147 |
87 88 90 91 92 121 124 146
|
fprodsplitsn |
|
148 |
107
|
prodeq2dv |
|
149 |
148 133
|
oveq12d |
|
150 |
86 147 149
|
3eqtrd |
|
151 |
150
|
sumeq2dv |
|
152 |
|
simpl |
|
153 |
152
|
fveq1d |
|
154 |
153
|
fveq2d |
|
155 |
154
|
prodeq2dv |
|
156 |
28 29 2 31 9
|
actfunsnf1o |
|
157 |
9
|
a1i |
|
158 |
|
simpr |
|
159 |
158
|
uneq1d |
|
160 |
|
vex |
|
161 |
160 66
|
unex |
|
162 |
161
|
a1i |
|
163 |
157 159 95 162
|
fvmptd |
|
164 |
155 21 156 163 82
|
fsumf1o |
|
165 |
|
simpl |
|
166 |
165
|
fveq1d |
|
167 |
166
|
fveq2d |
|
168 |
167
|
prodeq2dv |
|
169 |
168
|
oveq1d |
|
170 |
169
|
cbvsumv |
|
171 |
170
|
a1i |
|
172 |
151 164 171
|
3eqtr4d |
|
173 |
172
|
sumeq2dv |
|
174 |
11 84 173
|
3eqtrd |
|