Step |
Hyp |
Ref |
Expression |
1 |
|
pntpbnd.r |
|
2 |
|
pntpbnd1.e |
|
3 |
|
pntpbnd1.x |
|
4 |
|
pntpbnd1.y |
|
5 |
|
pntpbnd1a.1 |
|
6 |
|
pntpbnd1a.2 |
|
7 |
|
pntpbnd1a.3 |
|
8 |
5
|
nnrpd |
|
9 |
1
|
pntrf |
|
10 |
9
|
ffvelrni |
|
11 |
8 10
|
syl |
|
12 |
11 8
|
rerpdivcld |
|
13 |
12
|
recnd |
|
14 |
13
|
abscld |
|
15 |
8
|
relogcld |
|
16 |
15 8
|
rerpdivcld |
|
17 |
|
ioossre |
|
18 |
17 2
|
sseldi |
|
19 |
11
|
recnd |
|
20 |
5
|
nnred |
|
21 |
20
|
recnd |
|
22 |
5
|
nnne0d |
|
23 |
19 21 22
|
absdivd |
|
24 |
5
|
nnnn0d |
|
25 |
24
|
nn0ge0d |
|
26 |
20 25
|
absidd |
|
27 |
26
|
oveq2d |
|
28 |
23 27
|
eqtrd |
|
29 |
19
|
abscld |
|
30 |
5
|
peano2nnd |
|
31 |
|
vmacl |
|
32 |
30 31
|
syl |
|
33 |
|
peano2rem |
|
34 |
32 33
|
syl |
|
35 |
34
|
recnd |
|
36 |
35
|
abscld |
|
37 |
30
|
nnrpd |
|
38 |
1
|
pntrval |
|
39 |
37 38
|
syl |
|
40 |
1
|
pntrval |
|
41 |
8 40
|
syl |
|
42 |
39 41
|
oveq12d |
|
43 |
|
peano2re |
|
44 |
20 43
|
syl |
|
45 |
|
chpcl |
|
46 |
44 45
|
syl |
|
47 |
46
|
recnd |
|
48 |
44
|
recnd |
|
49 |
|
chpcl |
|
50 |
20 49
|
syl |
|
51 |
50
|
recnd |
|
52 |
47 48 51 21
|
sub4d |
|
53 |
32
|
recnd |
|
54 |
|
chpp1 |
|
55 |
24 54
|
syl |
|
56 |
51 53 55
|
mvrladdd |
|
57 |
|
ax-1cn |
|
58 |
|
pncan2 |
|
59 |
21 57 58
|
sylancl |
|
60 |
56 59
|
oveq12d |
|
61 |
42 52 60
|
3eqtrd |
|
62 |
61
|
fveq2d |
|
63 |
7 62
|
breqtrd |
|
64 |
|
1red |
|
65 |
64 15
|
resubcld |
|
66 |
|
0red |
|
67 |
|
2re |
|
68 |
|
eliooord |
|
69 |
2 68
|
syl |
|
70 |
69
|
simpld |
|
71 |
18 70
|
elrpd |
|
72 |
|
rerpdivcl |
|
73 |
67 71 72
|
sylancr |
|
74 |
67
|
a1i |
|
75 |
|
1lt2 |
|
76 |
75
|
a1i |
|
77 |
|
2cn |
|
78 |
77
|
div1i |
|
79 |
69
|
simprd |
|
80 |
|
0lt1 |
|
81 |
80
|
a1i |
|
82 |
|
2pos |
|
83 |
82
|
a1i |
|
84 |
|
ltdiv2 |
|
85 |
18 70 64 81 74 83 84
|
syl222anc |
|
86 |
79 85
|
mpbid |
|
87 |
78 86
|
eqbrtrrid |
|
88 |
64 74 73 76 87
|
lttrd |
|
89 |
73
|
rpefcld |
|
90 |
3 89
|
eqeltrid |
|
91 |
90
|
rpred |
|
92 |
90
|
rpxrd |
|
93 |
|
elioopnf |
|
94 |
92 93
|
syl |
|
95 |
4 94
|
mpbid |
|
96 |
95
|
simpld |
|
97 |
95
|
simprd |
|
98 |
6
|
simpld |
|
99 |
91 96 20 97 98
|
lttrd |
|
100 |
3 99
|
eqbrtrrid |
|
101 |
8
|
reeflogd |
|
102 |
100 101
|
breqtrrd |
|
103 |
|
eflt |
|
104 |
73 15 103
|
syl2anc |
|
105 |
102 104
|
mpbird |
|
106 |
64 73 15 88 105
|
lttrd |
|
107 |
64 15 106
|
ltled |
|
108 |
|
1re |
|
109 |
|
suble0 |
|
110 |
108 15 109
|
sylancr |
|
111 |
107 110
|
mpbird |
|
112 |
|
vmage0 |
|
113 |
30 112
|
syl |
|
114 |
65 66 32 111 113
|
letrd |
|
115 |
37
|
relogcld |
|
116 |
|
readdcl |
|
117 |
108 15 116
|
sylancr |
|
118 |
|
vmalelog |
|
119 |
30 118
|
syl |
|
120 |
74 20
|
remulcld |
|
121 |
|
epr |
|
122 |
|
rpmulcl |
|
123 |
121 8 122
|
sylancr |
|
124 |
123
|
rpred |
|
125 |
5
|
nnge1d |
|
126 |
64 20 20 125
|
leadd2dd |
|
127 |
21
|
2timesd |
|
128 |
126 127
|
breqtrrd |
|
129 |
|
ere |
|
130 |
|
egt2lt3 |
|
131 |
130
|
simpli |
|
132 |
67 129 131
|
ltleii |
|
133 |
132
|
a1i |
|
134 |
129
|
a1i |
|
135 |
5
|
nngt0d |
|
136 |
|
lemul1 |
|
137 |
74 134 20 135 136
|
syl112anc |
|
138 |
133 137
|
mpbid |
|
139 |
44 120 124 128 138
|
letrd |
|
140 |
37 123
|
logled |
|
141 |
139 140
|
mpbid |
|
142 |
|
relogmul |
|
143 |
121 8 142
|
sylancr |
|
144 |
|
loge |
|
145 |
144
|
oveq1i |
|
146 |
143 145
|
eqtrdi |
|
147 |
141 146
|
breqtrd |
|
148 |
32 115 117 119 147
|
letrd |
|
149 |
32 64 15
|
absdifled |
|
150 |
114 148 149
|
mpbir2and |
|
151 |
29 36 15 63 150
|
letrd |
|
152 |
29 15 8 151
|
lediv1dd |
|
153 |
28 152
|
eqbrtrd |
|
154 |
90
|
relogcld |
|
155 |
154 90
|
rerpdivcld |
|
156 |
64 73 88
|
ltled |
|
157 |
|
efle |
|
158 |
108 73 157
|
sylancr |
|
159 |
156 158
|
mpbid |
|
160 |
|
df-e |
|
161 |
159 160 3
|
3brtr4g |
|
162 |
144 107
|
eqbrtrid |
|
163 |
|
logleb |
|
164 |
121 8 163
|
sylancr |
|
165 |
162 164
|
mpbird |
|
166 |
|
logdivlt |
|
167 |
91 161 20 165 166
|
syl22anc |
|
168 |
99 167
|
mpbid |
|
169 |
3
|
fveq2i |
|
170 |
73
|
relogefd |
|
171 |
169 170
|
syl5eq |
|
172 |
171
|
oveq1d |
|
173 |
|
2rp |
|
174 |
|
rpdivcl |
|
175 |
173 71 174
|
sylancr |
|
176 |
175
|
rpcnd |
|
177 |
176
|
sqvald |
|
178 |
|
2cnd |
|
179 |
71
|
rpcnne0d |
|
180 |
|
div12 |
|
181 |
176 178 179 180
|
syl3anc |
|
182 |
177 181
|
eqtrd |
|
183 |
182
|
oveq1d |
|
184 |
175 71
|
rpdivcld |
|
185 |
184
|
rpcnd |
|
186 |
|
2ne0 |
|
187 |
186
|
a1i |
|
188 |
185 178 187
|
divcan3d |
|
189 |
183 188
|
eqtrd |
|
190 |
73
|
resqcld |
|
191 |
190
|
rehalfcld |
|
192 |
|
1rp |
|
193 |
|
rpaddcl |
|
194 |
192 175 193
|
sylancr |
|
195 |
194
|
rpred |
|
196 |
195 191
|
readdcld |
|
197 |
191 194
|
ltaddrp2d |
|
198 |
|
efgt1p2 |
|
199 |
175 198
|
syl |
|
200 |
199 3
|
breqtrrdi |
|
201 |
191 196 91 197 200
|
lttrd |
|
202 |
189 201
|
eqbrtrrd |
|
203 |
73 71 90 202
|
ltdiv23d |
|
204 |
172 203
|
eqbrtrd |
|
205 |
16 155 18 168 204
|
lttrd |
|
206 |
16 18 205
|
ltled |
|
207 |
14 16 18 153 206
|
letrd |
|