Step |
Hyp |
Ref |
Expression |
1 |
|
dvbdfbdioolem2.a |
|
2 |
|
dvbdfbdioolem2.b |
|
3 |
|
dvbdfbdioolem2.altb |
|
4 |
|
dvbdfbdioolem2.f |
|
5 |
|
dvbdfbdioolem2.dmdv |
|
6 |
|
dvbdfbdioolem2.k |
|
7 |
|
dvbdfbdioolem2.dvbd |
|
8 |
|
dvbdfbdioolem2.m |
|
9 |
4
|
ffvelrnda |
|
10 |
9
|
recnd |
|
11 |
10
|
abscld |
|
12 |
1
|
rexrd |
|
13 |
2
|
rexrd |
|
14 |
1 2
|
readdcld |
|
15 |
14
|
rehalfcld |
|
16 |
|
avglt1 |
|
17 |
1 2 16
|
syl2anc |
|
18 |
3 17
|
mpbid |
|
19 |
|
avglt2 |
|
20 |
1 2 19
|
syl2anc |
|
21 |
3 20
|
mpbid |
|
22 |
12 13 15 18 21
|
eliood |
|
23 |
4 22
|
ffvelrnd |
|
24 |
23
|
recnd |
|
25 |
24
|
abscld |
|
26 |
25
|
adantr |
|
27 |
11 26
|
resubcld |
|
28 |
6
|
adantr |
|
29 |
2
|
adantr |
|
30 |
1
|
adantr |
|
31 |
29 30
|
resubcld |
|
32 |
28 31
|
remulcld |
|
33 |
24
|
adantr |
|
34 |
10 33
|
subcld |
|
35 |
34
|
abscld |
|
36 |
10 33
|
abs2difd |
|
37 |
|
simpll |
|
38 |
15
|
rexrd |
|
39 |
38
|
ad2antrr |
|
40 |
13
|
ad2antrr |
|
41 |
|
elioore |
|
42 |
41
|
adantl |
|
43 |
42
|
adantr |
|
44 |
|
simpr |
|
45 |
12
|
adantr |
|
46 |
13
|
adantr |
|
47 |
|
simpr |
|
48 |
|
iooltub |
|
49 |
45 46 47 48
|
syl3anc |
|
50 |
49
|
adantr |
|
51 |
39 40 43 44 50
|
eliood |
|
52 |
1
|
adantr |
|
53 |
2
|
adantr |
|
54 |
4
|
adantr |
|
55 |
5
|
adantr |
|
56 |
6
|
adantr |
|
57 |
|
2fveq3 |
|
58 |
57
|
breq1d |
|
59 |
58
|
cbvralvw |
|
60 |
7 59
|
sylib |
|
61 |
60
|
adantr |
|
62 |
22
|
adantr |
|
63 |
|
simpr |
|
64 |
52 53 54 55 56 61 62 63
|
dvbdfbdioolem1 |
|
65 |
64
|
simprd |
|
66 |
37 51 65
|
syl2anc |
|
67 |
|
fveq2 |
|
68 |
67
|
eqcomd |
|
69 |
68
|
adantl |
|
70 |
24
|
adantr |
|
71 |
69 70
|
eqeltrd |
|
72 |
71 69
|
subeq0bd |
|
73 |
72
|
abs00bd |
|
74 |
6
|
adantr |
|
75 |
2
|
adantr |
|
76 |
1
|
adantr |
|
77 |
75 76
|
resubcld |
|
78 |
|
0red |
|
79 |
|
ioossre |
|
80 |
|
dvfre |
|
81 |
4 79 80
|
sylancl |
|
82 |
22 5
|
eleqtrrd |
|
83 |
81 82
|
ffvelrnd |
|
84 |
83
|
recnd |
|
85 |
84
|
abscld |
|
86 |
84
|
absge0d |
|
87 |
|
2fveq3 |
|
88 |
87
|
breq1d |
|
89 |
88
|
rspccva |
|
90 |
7 22 89
|
syl2anc |
|
91 |
78 85 6 86 90
|
letrd |
|
92 |
91
|
adantr |
|
93 |
2 1
|
resubcld |
|
94 |
1 2
|
posdifd |
|
95 |
3 94
|
mpbid |
|
96 |
78 93 95
|
ltled |
|
97 |
96
|
adantr |
|
98 |
74 77 92 97
|
mulge0d |
|
99 |
73 98
|
eqbrtrd |
|
100 |
99
|
ad4ant14 |
|
101 |
|
simpll |
|
102 |
42
|
ad2antrr |
|
103 |
15
|
ad3antrrr |
|
104 |
42
|
adantr |
|
105 |
15
|
ad2antrr |
|
106 |
|
simpr |
|
107 |
104 105 106
|
nltled |
|
108 |
107
|
adantr |
|
109 |
|
neqne |
|
110 |
109
|
adantl |
|
111 |
102 103 108 110
|
leneltd |
|
112 |
10 33
|
abssubd |
|
113 |
112
|
adantr |
|
114 |
1
|
ad2antrr |
|
115 |
2
|
ad2antrr |
|
116 |
4
|
ad2antrr |
|
117 |
5
|
ad2antrr |
|
118 |
6
|
ad2antrr |
|
119 |
60
|
ad2antrr |
|
120 |
47
|
adantr |
|
121 |
41
|
rexrd |
|
122 |
121
|
ad2antlr |
|
123 |
13
|
ad2antrr |
|
124 |
15
|
ad2antrr |
|
125 |
|
simpr |
|
126 |
21
|
ad2antrr |
|
127 |
122 123 124 125 126
|
eliood |
|
128 |
114 115 116 117 118 119 120 127
|
dvbdfbdioolem1 |
|
129 |
128
|
simprd |
|
130 |
113 129
|
eqbrtrd |
|
131 |
101 111 130
|
syl2anc |
|
132 |
100 131
|
pm2.61dan |
|
133 |
66 132
|
pm2.61dan |
|
134 |
27 35 32 36 133
|
letrd |
|
135 |
27 32 26 134
|
leadd1dd |
|
136 |
11
|
recnd |
|
137 |
26
|
recnd |
|
138 |
136 137
|
npcand |
|
139 |
138
|
eqcomd |
|
140 |
25
|
recnd |
|
141 |
6
|
recnd |
|
142 |
2
|
recnd |
|
143 |
1
|
recnd |
|
144 |
142 143
|
subcld |
|
145 |
141 144
|
mulcld |
|
146 |
140 145
|
addcomd |
|
147 |
8 146
|
syl5eq |
|
148 |
147
|
adantr |
|
149 |
135 139 148
|
3brtr4d |
|
150 |
149
|
ralrimiva |
|