Step |
Hyp |
Ref |
Expression |
1 |
|
pntibnd.r |
|
2 |
|
pntibndlem1.1 |
|
3 |
|
pntibndlem1.l |
|
4 |
|
pntibndlem3.2 |
|
5 |
|
pntibndlem3.3 |
|
6 |
|
pntibndlem3.k |
|
7 |
|
pntibndlem3.c |
|
8 |
|
pntibndlem3.4 |
|
9 |
|
pntibndlem3.6 |
|
10 |
|
pntibndlem3.5 |
|
11 |
|
2re |
|
12 |
|
1le2 |
|
13 |
|
chpdifbnd |
|
14 |
11 12 13
|
mp2an |
|
15 |
|
simpr |
|
16 |
|
ioossre |
|
17 |
16 8
|
sseldi |
|
18 |
|
eliooord |
|
19 |
8 18
|
syl |
|
20 |
19
|
simpld |
|
21 |
17 20
|
elrpd |
|
22 |
21
|
adantr |
|
23 |
|
4nn |
|
24 |
|
nnrp |
|
25 |
23 24
|
ax-mp |
|
26 |
|
rpdivcl |
|
27 |
22 25 26
|
sylancl |
|
28 |
15 27
|
rpdivcld |
|
29 |
28
|
rpred |
|
30 |
29
|
rpefcld |
|
31 |
9
|
adantr |
|
32 |
30 31
|
rpaddcld |
|
33 |
32
|
adantrr |
|
34 |
|
breq2 |
|
35 |
|
breq1 |
|
36 |
34 35
|
anbi12d |
|
37 |
|
fveq2 |
|
38 |
|
id |
|
39 |
37 38
|
oveq12d |
|
40 |
39
|
fveq2d |
|
41 |
40
|
breq1d |
|
42 |
36 41
|
anbi12d |
|
43 |
42
|
cbvrexvw |
|
44 |
|
breq1 |
|
45 |
|
oveq2 |
|
46 |
45
|
breq2d |
|
47 |
44 46
|
anbi12d |
|
48 |
47
|
anbi1d |
|
49 |
48
|
rexbidv |
|
50 |
43 49
|
syl5bb |
|
51 |
|
oveq1 |
|
52 |
51
|
breq2d |
|
53 |
52
|
anbi2d |
|
54 |
53
|
anbi1d |
|
55 |
54
|
rexbidv |
|
56 |
55
|
ralbidv |
|
57 |
10
|
ad2antrr |
|
58 |
5
|
adantr |
|
59 |
58
|
rpred |
|
60 |
|
remulcl |
|
61 |
11 59 60
|
sylancr |
|
62 |
|
2rp |
|
63 |
|
relogcl |
|
64 |
62 63
|
ax-mp |
|
65 |
|
readdcl |
|
66 |
61 64 65
|
sylancl |
|
67 |
7 66
|
eqeltrid |
|
68 |
67 22
|
rerpdivcld |
|
69 |
68
|
reefcld |
|
70 |
|
elicopnf |
|
71 |
69 70
|
syl |
|
72 |
71
|
simprbda |
|
73 |
72
|
rehalfcld |
|
74 |
22
|
rphalfcld |
|
75 |
59 74
|
rerpdivcld |
|
76 |
75
|
reefcld |
|
77 |
|
remulcl |
|
78 |
76 11 77
|
sylancl |
|
79 |
78
|
adantr |
|
80 |
69
|
adantr |
|
81 |
75
|
recnd |
|
82 |
64
|
recni |
|
83 |
|
efadd |
|
84 |
81 82 83
|
sylancl |
|
85 |
|
reeflog |
|
86 |
62 85
|
ax-mp |
|
87 |
86
|
oveq2i |
|
88 |
84 87
|
eqtrdi |
|
89 |
64
|
a1i |
|
90 |
|
rerpdivcl |
|
91 |
64 22 90
|
sylancr |
|
92 |
82
|
div1i |
|
93 |
19
|
simprd |
|
94 |
93
|
adantr |
|
95 |
17
|
adantr |
|
96 |
|
1re |
|
97 |
|
ltle |
|
98 |
95 96 97
|
sylancl |
|
99 |
94 98
|
mpd |
|
100 |
22
|
rpregt0d |
|
101 |
|
1rp |
|
102 |
|
rpregt0 |
|
103 |
101 102
|
mp1i |
|
104 |
|
1lt2 |
|
105 |
|
rplogcl |
|
106 |
11 104 105
|
mp2an |
|
107 |
|
rpregt0 |
|
108 |
106 107
|
mp1i |
|
109 |
|
lediv2 |
|
110 |
100 103 108 109
|
syl3anc |
|
111 |
99 110
|
mpbid |
|
112 |
92 111
|
eqbrtrrid |
|
113 |
89 91 75 112
|
leadd2dd |
|
114 |
7
|
oveq1i |
|
115 |
61
|
recnd |
|
116 |
82
|
a1i |
|
117 |
|
rpcnne0 |
|
118 |
22 117
|
syl |
|
119 |
|
divdir |
|
120 |
115 116 118 119
|
syl3anc |
|
121 |
114 120
|
syl5eq |
|
122 |
11
|
recni |
|
123 |
59
|
recnd |
|
124 |
|
mulcom |
|
125 |
122 123 124
|
sylancr |
|
126 |
125
|
oveq1d |
|
127 |
|
rpcnne0 |
|
128 |
62 127
|
mp1i |
|
129 |
|
divdiv2 |
|
130 |
123 118 128 129
|
syl3anc |
|
131 |
126 130
|
eqtr4d |
|
132 |
131
|
oveq1d |
|
133 |
121 132
|
eqtrd |
|
134 |
113 133
|
breqtrrd |
|
135 |
|
readdcl |
|
136 |
75 64 135
|
sylancl |
|
137 |
|
efle |
|
138 |
136 68 137
|
syl2anc |
|
139 |
134 138
|
mpbid |
|
140 |
88 139
|
eqbrtrrd |
|
141 |
140
|
adantr |
|
142 |
71
|
simplbda |
|
143 |
79 80 72 141 142
|
letrd |
|
144 |
76
|
adantr |
|
145 |
|
rpregt0 |
|
146 |
62 145
|
mp1i |
|
147 |
|
lemuldiv |
|
148 |
144 72 146 147
|
syl3anc |
|
149 |
143 148
|
mpbid |
|
150 |
6 149
|
eqbrtrid |
|
151 |
6 144
|
eqeltrid |
|
152 |
|
elicopnf |
|
153 |
151 152
|
syl |
|
154 |
73 150 153
|
mpbir2and |
|
155 |
154
|
adantrr |
|
156 |
155
|
adantlrr |
|
157 |
56 57 156
|
rspcdva |
|
158 |
|
elioore |
|
159 |
158
|
ad2antll |
|
160 |
31
|
rpred |
|
161 |
160
|
adantr |
|
162 |
29
|
reefcld |
|
163 |
162 160
|
readdcld |
|
164 |
163
|
adantr |
|
165 |
160 30
|
ltaddrp2d |
|
166 |
165
|
adantr |
|
167 |
|
eliooord |
|
168 |
167
|
simpld |
|
169 |
168
|
ad2antll |
|
170 |
161 164 159 166 169
|
lttrd |
|
171 |
161
|
rexrd |
|
172 |
|
elioopnf |
|
173 |
171 172
|
syl |
|
174 |
159 170 173
|
mpbir2and |
|
175 |
174
|
adantlrr |
|
176 |
50 157 175
|
rspcdva |
|
177 |
2
|
ad2antrr |
|
178 |
|
fveq2 |
|
179 |
|
id |
|
180 |
178 179
|
oveq12d |
|
181 |
180
|
fveq2d |
|
182 |
181
|
breq1d |
|
183 |
182
|
cbvralvw |
|
184 |
4 183
|
sylib |
|
185 |
184
|
ad2antrr |
|
186 |
5
|
ad2antrr |
|
187 |
8
|
ad2antrr |
|
188 |
9
|
ad2antrr |
|
189 |
|
simprrl |
|
190 |
|
simplrl |
|
191 |
|
simplrr |
|
192 |
|
eqid |
|
193 |
|
simprll |
|
194 |
|
simprlr |
|
195 |
|
simprrr |
|
196 |
1 177 3 185 186 6 7 187 188 189 190 191 192 193 194 195
|
pntibndlem2 |
|
197 |
196
|
anassrs |
|
198 |
176 197
|
rexlimddv |
|
199 |
198
|
ralrimivva |
|
200 |
|
oveq1 |
|
201 |
200
|
raleqdv |
|
202 |
201
|
ralbidv |
|
203 |
202
|
rspcev |
|
204 |
33 199 203
|
syl2anc |
|
205 |
204
|
rexlimdvaa |
|
206 |
14 205
|
mpi |
|