Step |
Hyp |
Ref |
Expression |
1 |
|
sge0seq.m |
|
2 |
|
sge0seq.z |
|
3 |
|
sge0seq.f |
|
4 |
|
sge0seq.g |
|
5 |
|
rge0ssre |
|
6 |
3
|
ffvelrnda |
|
7 |
5 6
|
sselid |
|
8 |
|
readdcl |
|
9 |
8
|
adantl |
|
10 |
2 1 7 9
|
seqf |
|
11 |
4
|
a1i |
|
12 |
11
|
feq1d |
|
13 |
10 12
|
mpbird |
|
14 |
13
|
frnd |
|
15 |
|
ressxr |
|
16 |
15
|
a1i |
|
17 |
14 16
|
sstrd |
|
18 |
2
|
fvexi |
|
19 |
18
|
a1i |
|
20 |
|
icossicc |
|
21 |
20
|
a1i |
|
22 |
3 21
|
fssd |
|
23 |
19 22
|
sge0xrcl |
|
24 |
|
simpr |
|
25 |
13
|
ffnd |
|
26 |
|
fvelrnb |
|
27 |
25 26
|
syl |
|
28 |
27
|
adantr |
|
29 |
24 28
|
mpbid |
|
30 |
20 6
|
sselid |
|
31 |
|
elfzuz |
|
32 |
31 2
|
eleqtrrdi |
|
33 |
32
|
ssriv |
|
34 |
33
|
a1i |
|
35 |
19 30 34
|
sge0lessmpt |
|
36 |
35
|
3ad2ant1 |
|
37 |
|
fzfid |
|
38 |
32 6
|
sylan2 |
|
39 |
37 38
|
sge0fsummpt |
|
40 |
39
|
3ad2ant1 |
|
41 |
|
simpll |
|
42 |
32
|
adantl |
|
43 |
|
eqidd |
|
44 |
41 42 43
|
syl2anc |
|
45 |
2
|
eleq2i |
|
46 |
45
|
biimpi |
|
47 |
46
|
adantl |
|
48 |
7
|
recnd |
|
49 |
41 42 48
|
syl2anc |
|
50 |
44 47 49
|
fsumser |
|
51 |
50
|
3adant3 |
|
52 |
40 51
|
eqtrd |
|
53 |
4
|
eqcomi |
|
54 |
53
|
fveq1i |
|
55 |
54
|
a1i |
|
56 |
|
simp3 |
|
57 |
52 55 56
|
3eqtrrd |
|
58 |
3
|
feqmptd |
|
59 |
58
|
fveq2d |
|
60 |
59
|
3ad2ant1 |
|
61 |
57 60
|
breq12d |
|
62 |
36 61
|
mpbird |
|
63 |
62
|
3exp |
|
64 |
63
|
adantr |
|
65 |
64
|
rexlimdv |
|
66 |
29 65
|
mpd |
|
67 |
66
|
ralrimiva |
|
68 |
|
nfv |
|
69 |
18
|
a1i |
|
70 |
6
|
ad4ant14 |
|
71 |
|
simplr |
|
72 |
|
simpr |
|
73 |
59
|
adantr |
|
74 |
72 73
|
breqtrd |
|
75 |
74
|
adantlr |
|
76 |
68 69 70 71 75
|
sge0gtfsumgt |
|
77 |
1
|
3ad2ant1 |
|
78 |
|
elpwinss |
|
79 |
78
|
3ad2ant2 |
|
80 |
|
elinel2 |
|
81 |
80
|
3ad2ant2 |
|
82 |
77 2 79 81
|
uzfissfz |
|
83 |
82
|
3adant1r |
|
84 |
|
simpl1r |
|
85 |
80
|
adantl |
|
86 |
58 7
|
fmpt3d |
|
87 |
86
|
ad2antrr |
|
88 |
78
|
sselda |
|
89 |
88
|
adantll |
|
90 |
87 89
|
ffvelrnd |
|
91 |
85 90
|
fsumrecl |
|
92 |
91
|
ad4ant13 |
|
93 |
92
|
3adantl3 |
|
94 |
32 7
|
sylan2 |
|
95 |
37 94
|
fsumrecl |
|
96 |
95
|
ad3antrrr |
|
97 |
96
|
3adantl3 |
|
98 |
|
simpl3 |
|
99 |
37
|
adantr |
|
100 |
94
|
adantlr |
|
101 |
|
0xr |
|
102 |
101
|
a1i |
|
103 |
|
pnfxr |
|
104 |
103
|
a1i |
|
105 |
|
icogelb |
|
106 |
102 104 6 105
|
syl3anc |
|
107 |
32 106
|
sylan2 |
|
108 |
107
|
adantlr |
|
109 |
|
simpr |
|
110 |
99 100 108 109
|
fsumless |
|
111 |
110
|
adantlr |
|
112 |
111
|
3ad2antl1 |
|
113 |
84 93 97 98 112
|
ltletrd |
|
114 |
113
|
ex |
|
115 |
114
|
reximdv |
|
116 |
83 115
|
mpd |
|
117 |
116
|
3exp |
|
118 |
117
|
adantr |
|
119 |
118
|
rexlimdv |
|
120 |
76 119
|
mpd |
|
121 |
10
|
ffnd |
|
122 |
121
|
adantr |
|
123 |
47 45
|
sylibr |
|
124 |
|
fnfvelrn |
|
125 |
122 123 124
|
syl2anc |
|
126 |
4
|
a1i |
|
127 |
126
|
rneqd |
|
128 |
50 127
|
eleq12d |
|
129 |
125 128
|
mpbird |
|
130 |
129
|
adantlr |
|
131 |
130
|
3adant3 |
|
132 |
|
simp3 |
|
133 |
|
breq2 |
|
134 |
133
|
rspcev |
|
135 |
131 132 134
|
syl2anc |
|
136 |
135
|
3exp |
|
137 |
136
|
rexlimdv |
|
138 |
137
|
adantr |
|
139 |
120 138
|
mpd |
|
140 |
139
|
ex |
|
141 |
140
|
ralrimiva |
|
142 |
|
supxr2 |
|
143 |
17 23 67 141 142
|
syl22anc |
|
144 |
143
|
eqcomd |
|