Step |
Hyp |
Ref |
Expression |
1 |
|
ovolicc.1 |
|
2 |
|
ovolicc.2 |
|
3 |
|
ovolicc.3 |
|
4 |
|
ovolicc1.4 |
|
5 |
|
iccssre |
|
6 |
1 2 5
|
syl2anc |
|
7 |
|
ovolcl |
|
8 |
6 7
|
syl |
|
9 |
|
df-br |
|
10 |
3 9
|
sylib |
|
11 |
1 2
|
opelxpd |
|
12 |
10 11
|
elind |
|
13 |
12
|
adantr |
|
14 |
|
0le0 |
|
15 |
|
df-br |
|
16 |
14 15
|
mpbi |
|
17 |
|
0re |
|
18 |
|
opelxpi |
|
19 |
17 17 18
|
mp2an |
|
20 |
16 19
|
elini |
|
21 |
|
ifcl |
|
22 |
13 20 21
|
sylancl |
|
23 |
22 4
|
fmptd |
|
24 |
|
eqid |
|
25 |
|
eqid |
|
26 |
24 25
|
ovolsf |
|
27 |
23 26
|
syl |
|
28 |
27
|
frnd |
|
29 |
|
icossxr |
|
30 |
28 29
|
sstrdi |
|
31 |
|
supxrcl |
|
32 |
30 31
|
syl |
|
33 |
2 1
|
resubcld |
|
34 |
33
|
rexrd |
|
35 |
|
1nn |
|
36 |
35
|
a1i |
|
37 |
|
op1stg |
|
38 |
1 2 37
|
syl2anc |
|
39 |
38
|
adantr |
|
40 |
|
elicc2 |
|
41 |
1 2 40
|
syl2anc |
|
42 |
41
|
biimpa |
|
43 |
42
|
simp2d |
|
44 |
39 43
|
eqbrtrd |
|
45 |
42
|
simp3d |
|
46 |
|
op2ndg |
|
47 |
1 2 46
|
syl2anc |
|
48 |
47
|
adantr |
|
49 |
45 48
|
breqtrrd |
|
50 |
|
fveq2 |
|
51 |
|
iftrue |
|
52 |
|
opex |
|
53 |
51 4 52
|
fvmpt |
|
54 |
35 53
|
ax-mp |
|
55 |
50 54
|
eqtrdi |
|
56 |
55
|
fveq2d |
|
57 |
56
|
breq1d |
|
58 |
55
|
fveq2d |
|
59 |
58
|
breq2d |
|
60 |
57 59
|
anbi12d |
|
61 |
60
|
rspcev |
|
62 |
36 44 49 61
|
syl12anc |
|
63 |
62
|
ralrimiva |
|
64 |
|
ovolficc |
|
65 |
6 23 64
|
syl2anc |
|
66 |
63 65
|
mpbird |
|
67 |
25
|
ovollb2 |
|
68 |
23 66 67
|
syl2anc |
|
69 |
|
addid1 |
|
70 |
69
|
adantl |
|
71 |
|
nnuz |
|
72 |
35 71
|
eleqtri |
|
73 |
72
|
a1i |
|
74 |
|
simpr |
|
75 |
74 71
|
eleqtrdi |
|
76 |
|
rge0ssre |
|
77 |
27
|
adantr |
|
78 |
|
ffvelrn |
|
79 |
77 35 78
|
sylancl |
|
80 |
76 79
|
sseldi |
|
81 |
80
|
recnd |
|
82 |
23
|
ad2antrr |
|
83 |
|
elfzuz |
|
84 |
83
|
adantl |
|
85 |
|
df-2 |
|
86 |
85
|
fveq2i |
|
87 |
84 86
|
eleqtrrdi |
|
88 |
|
eluz2nn |
|
89 |
87 88
|
syl |
|
90 |
24
|
ovolfsval |
|
91 |
82 89 90
|
syl2anc |
|
92 |
|
eqeq1 |
|
93 |
92
|
ifbid |
|
94 |
|
opex |
|
95 |
52 94
|
ifex |
|
96 |
93 4 95
|
fvmpt |
|
97 |
89 96
|
syl |
|
98 |
|
eluz2b3 |
|
99 |
98
|
simprbi |
|
100 |
87 99
|
syl |
|
101 |
100
|
neneqd |
|
102 |
101
|
iffalsed |
|
103 |
97 102
|
eqtrd |
|
104 |
103
|
fveq2d |
|
105 |
|
c0ex |
|
106 |
105 105
|
op2nd |
|
107 |
104 106
|
eqtrdi |
|
108 |
103
|
fveq2d |
|
109 |
105 105
|
op1st |
|
110 |
108 109
|
eqtrdi |
|
111 |
107 110
|
oveq12d |
|
112 |
|
0m0e0 |
|
113 |
111 112
|
eqtrdi |
|
114 |
91 113
|
eqtrd |
|
115 |
70 73 75 81 114
|
seqid2 |
|
116 |
|
1z |
|
117 |
23
|
adantr |
|
118 |
24
|
ovolfsval |
|
119 |
117 35 118
|
sylancl |
|
120 |
54
|
fveq2i |
|
121 |
47
|
adantr |
|
122 |
120 121
|
syl5eq |
|
123 |
54
|
fveq2i |
|
124 |
38
|
adantr |
|
125 |
123 124
|
syl5eq |
|
126 |
122 125
|
oveq12d |
|
127 |
119 126
|
eqtrd |
|
128 |
116 127
|
seq1i |
|
129 |
115 128
|
eqtr3d |
|
130 |
33
|
leidd |
|
131 |
130
|
adantr |
|
132 |
129 131
|
eqbrtrd |
|
133 |
132
|
ralrimiva |
|
134 |
27
|
ffnd |
|
135 |
|
breq1 |
|
136 |
135
|
ralrn |
|
137 |
134 136
|
syl |
|
138 |
133 137
|
mpbird |
|
139 |
|
supxrleub |
|
140 |
30 34 139
|
syl2anc |
|
141 |
138 140
|
mpbird |
|
142 |
8 32 34 68 141
|
xrletrd |
|