Step |
Hyp |
Ref |
Expression |
1 |
|
sge0xadd.kph |
|
2 |
|
sge0xadd.a |
|
3 |
|
sge0xadd.b |
|
4 |
|
sge0xadd.c |
|
5 |
|
simpr |
|
6 |
5
|
oveq1d |
|
7 |
1 2 4
|
sge0xrclmpt |
|
8 |
|
eqid |
|
9 |
1 4 8
|
fmptdf |
|
10 |
2 9
|
sge0nemnf |
|
11 |
|
xaddpnf2 |
|
12 |
7 10 11
|
syl2anc |
|
13 |
12
|
adantr |
|
14 |
|
ge0xaddcl |
|
15 |
3 4 14
|
syl2anc |
|
16 |
1 2 15
|
sge0xrclmpt |
|
17 |
16
|
adantr |
|
18 |
|
id |
|
19 |
18
|
eqcomd |
|
20 |
19
|
adantl |
|
21 |
2
|
elexd |
|
22 |
|
iccssxr |
|
23 |
22 3
|
sseldi |
|
24 |
23 4
|
xadd0ge |
|
25 |
1 21 3 15 24
|
sge0lempt |
|
26 |
25
|
adantr |
|
27 |
20 26
|
eqbrtrd |
|
28 |
17 27
|
xrgepnfd |
|
29 |
28
|
eqcomd |
|
30 |
6 13 29
|
3eqtrrd |
|
31 |
|
simpl |
|
32 |
|
simpr |
|
33 |
|
eqid |
|
34 |
1 3 33
|
fmptdf |
|
35 |
2 34
|
sge0repnf |
|
36 |
35
|
adantr |
|
37 |
32 36
|
mpbird |
|
38 |
|
simpr |
|
39 |
38
|
oveq2d |
|
40 |
2 34
|
sge0xrcl |
|
41 |
2 34
|
sge0nemnf |
|
42 |
|
xaddpnf1 |
|
43 |
40 41 42
|
syl2anc |
|
44 |
43
|
adantr |
|
45 |
16
|
adantr |
|
46 |
|
id |
|
47 |
46
|
eqcomd |
|
48 |
47
|
adantl |
|
49 |
22 4
|
sseldi |
|
50 |
49 3
|
xadd0ge2 |
|
51 |
1 2 4 15 50
|
sge0lempt |
|
52 |
51
|
adantr |
|
53 |
48 52
|
eqbrtrd |
|
54 |
45 53
|
xrgepnfd |
|
55 |
54
|
eqcomd |
|
56 |
39 44 55
|
3eqtrrd |
|
57 |
56
|
adantlr |
|
58 |
|
simpl |
|
59 |
|
simpr |
|
60 |
2 9
|
sge0repnf |
|
61 |
60
|
adantr |
|
62 |
59 61
|
mpbird |
|
63 |
62
|
adantlr |
|
64 |
2
|
ad2antrr |
|
65 |
|
nfcv |
|
66 |
|
nfmpt1 |
|
67 |
65 66
|
nffv |
|
68 |
|
nfcv |
|
69 |
67 68
|
nfel |
|
70 |
1 69
|
nfan |
|
71 |
|
nfv |
|
72 |
70 71
|
nfan |
|
73 |
|
nfcsb1v |
|
74 |
73
|
nfel1 |
|
75 |
72 74
|
nfim |
|
76 |
|
eleq1w |
|
77 |
76
|
anbi2d |
|
78 |
|
csbeq1a |
|
79 |
78
|
eleq1d |
|
80 |
77 79
|
imbi12d |
|
81 |
2
|
adantr |
|
82 |
3
|
adantlr |
|
83 |
|
simpr |
|
84 |
70 81 82 83
|
sge0rernmpt |
|
85 |
75 80 84
|
chvarfv |
|
86 |
85
|
adantlr |
|
87 |
|
nfmpt1 |
|
88 |
65 87
|
nffv |
|
89 |
88 68
|
nfel |
|
90 |
1 89
|
nfan |
|
91 |
90 71
|
nfan |
|
92 |
|
nfcsb1v |
|
93 |
92
|
nfel1 |
|
94 |
91 93
|
nfim |
|
95 |
76
|
anbi2d |
|
96 |
|
csbeq1a |
|
97 |
96
|
eleq1d |
|
98 |
95 97
|
imbi12d |
|
99 |
2
|
adantr |
|
100 |
4
|
adantlr |
|
101 |
|
simpr |
|
102 |
90 99 100 101
|
sge0rernmpt |
|
103 |
94 98 102
|
chvarfv |
|
104 |
103
|
adantllr |
|
105 |
|
nfcv |
|
106 |
105 73 78
|
cbvmpt |
|
107 |
106
|
fveq2i |
|
108 |
|
simplr |
|
109 |
107 108
|
eqeltrrid |
|
110 |
|
nfcv |
|
111 |
110 92 96
|
cbvmpt |
|
112 |
111
|
fveq2i |
|
113 |
|
simpr |
|
114 |
112 113
|
eqeltrrid |
|
115 |
64 86 104 109 114
|
sge0xaddlem2 |
|
116 |
|
nfcv |
|
117 |
|
nfcv |
|
118 |
73 117 92
|
nfov |
|
119 |
78 96
|
oveq12d |
|
120 |
116 118 119
|
cbvmpt |
|
121 |
120
|
fveq2i |
|
122 |
107 112
|
oveq12i |
|
123 |
121 122
|
eqeq12i |
|
124 |
115 123
|
sylibr |
|
125 |
58 63 124
|
syl2anc |
|
126 |
57 125
|
pm2.61dan |
|
127 |
31 37 126
|
syl2anc |
|
128 |
30 127
|
pm2.61dan |
|