Step |
Hyp |
Ref |
Expression |
1 |
|
iseralt.1 |
|
2 |
|
iseralt.2 |
|
3 |
|
iseralt.3 |
|
4 |
|
iseralt.4 |
|
5 |
|
iseralt.5 |
|
6 |
|
iseralt.6 |
|
7 |
|
seqex |
|
8 |
7
|
a1i |
|
9 |
|
climrel |
|
10 |
9
|
brrelex1i |
|
11 |
5 10
|
syl |
|
12 |
|
eqidd |
|
13 |
3
|
ffvelrnda |
|
14 |
13
|
recnd |
|
15 |
1 2 11 12 14
|
clim0c |
|
16 |
5 15
|
mpbid |
|
17 |
|
simpr |
|
18 |
17 1
|
eleqtrdi |
|
19 |
|
eluzelz |
|
20 |
|
uzid |
|
21 |
18 19 20
|
3syl |
|
22 |
|
peano2uz |
|
23 |
|
2fveq3 |
|
24 |
23
|
breq1d |
|
25 |
24
|
rspcv |
|
26 |
21 22 25
|
3syl |
|
27 |
|
eluzelz |
|
28 |
27
|
ad2antll |
|
29 |
28
|
zcnd |
|
30 |
19 1
|
eleq2s |
|
31 |
30
|
ad2antrl |
|
32 |
31
|
zcnd |
|
33 |
29 32
|
subcld |
|
34 |
|
2cnd |
|
35 |
|
2ne0 |
|
36 |
35
|
a1i |
|
37 |
33 34 36
|
divcan2d |
|
38 |
37
|
oveq2d |
|
39 |
32 29
|
pncan3d |
|
40 |
38 39
|
eqtr2d |
|
41 |
40
|
adantr |
|
42 |
41
|
fveq2d |
|
43 |
42
|
fvoveq1d |
|
44 |
|
simpll |
|
45 |
|
simpl |
|
46 |
45
|
ad2antlr |
|
47 |
|
simpr |
|
48 |
28 31
|
zsubcld |
|
49 |
48
|
zred |
|
50 |
|
2rp |
|
51 |
50
|
a1i |
|
52 |
|
eluzle |
|
53 |
52
|
ad2antll |
|
54 |
28
|
zred |
|
55 |
31
|
zred |
|
56 |
54 55
|
subge0d |
|
57 |
53 56
|
mpbird |
|
58 |
49 51 57
|
divge0d |
|
59 |
58
|
adantr |
|
60 |
|
elnn0z |
|
61 |
47 59 60
|
sylanbrc |
|
62 |
1 2 3 4 5 6
|
iseraltlem3 |
|
63 |
62
|
simpld |
|
64 |
44 46 61 63
|
syl3anc |
|
65 |
43 64
|
eqbrtrd |
|
66 |
|
2div2e1 |
|
67 |
66
|
oveq2i |
|
68 |
|
peano2cn |
|
69 |
33 68
|
syl |
|
70 |
69 34 34 36
|
divsubdird |
|
71 |
|
df-2 |
|
72 |
71
|
oveq2i |
|
73 |
|
ax-1cn |
|
74 |
73
|
a1i |
|
75 |
33 74 74
|
pnpcan2d |
|
76 |
72 75
|
syl5eq |
|
77 |
76
|
oveq1d |
|
78 |
70 77
|
eqtr3d |
|
79 |
67 78
|
eqtr3id |
|
80 |
79
|
oveq2d |
|
81 |
|
subcl |
|
82 |
33 73 81
|
sylancl |
|
83 |
82 34 36
|
divcan2d |
|
84 |
29 32 74
|
sub32d |
|
85 |
80 83 84
|
3eqtrd |
|
86 |
85
|
oveq2d |
|
87 |
|
subcl |
|
88 |
29 73 87
|
sylancl |
|
89 |
32 88
|
pncan3d |
|
90 |
86 89
|
eqtrd |
|
91 |
90
|
oveq1d |
|
92 |
|
npcan |
|
93 |
29 73 92
|
sylancl |
|
94 |
91 93
|
eqtr2d |
|
95 |
94
|
adantr |
|
96 |
95
|
fveq2d |
|
97 |
96
|
fvoveq1d |
|
98 |
|
simpll |
|
99 |
45
|
ad2antlr |
|
100 |
|
simpr |
|
101 |
|
uznn0sub |
|
102 |
101
|
ad2antll |
|
103 |
|
nn0p1nn |
|
104 |
102 103
|
syl |
|
105 |
104
|
nnrpd |
|
106 |
105
|
rphalfcld |
|
107 |
106
|
rpgt0d |
|
108 |
107
|
adantr |
|
109 |
|
elnnz |
|
110 |
100 108 109
|
sylanbrc |
|
111 |
|
nnm1nn0 |
|
112 |
110 111
|
syl |
|
113 |
1 2 3 4 5 6
|
iseraltlem3 |
|
114 |
113
|
simprd |
|
115 |
98 99 112 114
|
syl3anc |
|
116 |
97 115
|
eqbrtrd |
|
117 |
|
zeo |
|
118 |
48 117
|
syl |
|
119 |
65 116 118
|
mpjaodan |
|
120 |
1
|
peano2uzs |
|
121 |
120
|
adantr |
|
122 |
|
ffvelrn |
|
123 |
3 121 122
|
syl2an |
|
124 |
1 2 3 4 5
|
iseraltlem1 |
|
125 |
121 124
|
sylan2 |
|
126 |
123 125
|
absidd |
|
127 |
119 126
|
breqtrrd |
|
128 |
127
|
adantlr |
|
129 |
|
neg1rr |
|
130 |
129
|
a1i |
|
131 |
|
neg1ne0 |
|
132 |
131
|
a1i |
|
133 |
|
eluzelz |
|
134 |
133 1
|
eleq2s |
|
135 |
134
|
adantl |
|
136 |
130 132 135
|
reexpclzd |
|
137 |
3
|
ffvelrnda |
|
138 |
136 137
|
remulcld |
|
139 |
6 138
|
eqeltrd |
|
140 |
1 2 139
|
serfre |
|
141 |
1
|
uztrn2 |
|
142 |
|
ffvelrn |
|
143 |
140 141 142
|
syl2an |
|
144 |
|
ffvelrn |
|
145 |
140 45 144
|
syl2an |
|
146 |
143 145
|
resubcld |
|
147 |
146
|
recnd |
|
148 |
147
|
abscld |
|
149 |
148
|
adantlr |
|
150 |
126 123
|
eqeltrd |
|
151 |
150
|
adantlr |
|
152 |
|
rpre |
|
153 |
152
|
ad2antlr |
|
154 |
|
lelttr |
|
155 |
149 151 153 154
|
syl3anc |
|
156 |
128 155
|
mpand |
|
157 |
140
|
adantr |
|
158 |
157 141 142
|
syl2an |
|
159 |
156 158
|
jctild |
|
160 |
159
|
anassrs |
|
161 |
160
|
ralrimdva |
|
162 |
26 161
|
syld |
|
163 |
162
|
reximdva |
|
164 |
163
|
ralimdva |
|
165 |
16 164
|
mpd |
|
166 |
1 8 165
|
caurcvg2 |
|