Step |
Hyp |
Ref |
Expression |
1 |
|
hbt.p |
|
2 |
|
lnrring |
|
3 |
1
|
ply1ring |
|
4 |
2 3
|
syl |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
5 6
|
islnr3 |
|
8 |
7
|
simprbi |
|
9 |
8
|
adantr |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
1 10 11 6
|
hbtlem7 |
|
13 |
2 12
|
sylan |
|
14 |
2
|
ad2antrr |
|
15 |
|
simplr |
|
16 |
|
simpr |
|
17 |
|
peano2nn0 |
|
18 |
17
|
adantl |
|
19 |
|
nn0re |
|
20 |
19
|
lep1d |
|
21 |
20
|
adantl |
|
22 |
1 10 11 14 15 16 18 21
|
hbtlem4 |
|
23 |
22
|
ralrimiva |
|
24 |
|
nacsfix |
|
25 |
9 13 23 24
|
syl3anc |
|
26 |
|
fzfi |
|
27 |
|
eqid |
|
28 |
|
simpll |
|
29 |
|
simplr |
|
30 |
|
elfznn0 |
|
31 |
30
|
adantl |
|
32 |
1 10 11 27 28 29 31
|
hbtlem6 |
|
33 |
32
|
ralrimiva |
|
34 |
|
2fveq3 |
|
35 |
34
|
fveq1d |
|
36 |
35
|
sseq2d |
|
37 |
36
|
ac6sfi |
|
38 |
26 33 37
|
sylancr |
|
39 |
38
|
adantr |
|
40 |
|
frn |
|
41 |
40
|
ad2antrl |
|
42 |
|
inss1 |
|
43 |
41 42
|
sstrdi |
|
44 |
43
|
unissd |
|
45 |
|
unipw |
|
46 |
44 45
|
sseqtrdi |
|
47 |
|
simpllr |
|
48 |
|
eqid |
|
49 |
48 10
|
lidlss |
|
50 |
47 49
|
syl |
|
51 |
46 50
|
sstrd |
|
52 |
|
fvex |
|
53 |
52
|
elpw2 |
|
54 |
51 53
|
sylibr |
|
55 |
|
simprl |
|
56 |
|
ffn |
|
57 |
|
fniunfv |
|
58 |
55 56 57
|
3syl |
|
59 |
|
inss2 |
|
60 |
55
|
ffvelrnda |
|
61 |
59 60
|
sseldi |
|
62 |
61
|
ralrimiva |
|
63 |
|
iunfi |
|
64 |
26 62 63
|
sylancr |
|
65 |
58 64
|
eqeltrrd |
|
66 |
54 65
|
elind |
|
67 |
2
|
ad3antrrr |
|
68 |
4
|
ad3antrrr |
|
69 |
27 48 10
|
rspcl |
|
70 |
68 51 69
|
syl2anc |
|
71 |
27 10
|
rspssp |
|
72 |
68 47 46 71
|
syl3anc |
|
73 |
|
nn0re |
|
74 |
73
|
adantl |
|
75 |
|
simplrl |
|
76 |
75
|
adantr |
|
77 |
76
|
nn0red |
|
78 |
|
simprl |
|
79 |
|
simprr |
|
80 |
75
|
adantr |
|
81 |
|
fznn0 |
|
82 |
80 81
|
syl |
|
83 |
78 79 82
|
mpbir2and |
|
84 |
|
simplrr |
|
85 |
|
fveq2 |
|
86 |
|
2fveq3 |
|
87 |
86
|
fveq2d |
|
88 |
|
id |
|
89 |
87 88
|
fveq12d |
|
90 |
85 89
|
sseq12d |
|
91 |
90
|
rspcva |
|
92 |
83 84 91
|
syl2anc |
|
93 |
67
|
adantr |
|
94 |
|
fvssunirn |
|
95 |
94 51
|
sstrid |
|
96 |
27 48 10
|
rspcl |
|
97 |
68 95 96
|
syl2anc |
|
98 |
97
|
adantr |
|
99 |
70
|
adantr |
|
100 |
67 3
|
syl |
|
101 |
100
|
adantr |
|
102 |
27 48
|
rspssid |
|
103 |
68 51 102
|
syl2anc |
|
104 |
103
|
adantr |
|
105 |
94 104
|
sstrid |
|
106 |
27 10
|
rspssp |
|
107 |
101 99 105 106
|
syl3anc |
|
108 |
1 10 11 93 98 99 107 78
|
hbtlem3 |
|
109 |
92 108
|
sstrd |
|
110 |
109
|
anassrs |
|
111 |
|
nn0z |
|
112 |
111
|
adantr |
|
113 |
|
nn0z |
|
114 |
113
|
ad2antrl |
|
115 |
|
simprr |
|
116 |
|
eluz2 |
|
117 |
112 114 115 116
|
syl3anbrc |
|
118 |
75 117
|
sylan |
|
119 |
|
simprr |
|
120 |
119
|
ad2antrr |
|
121 |
|
fveqeq2 |
|
122 |
121
|
rspcva |
|
123 |
118 120 122
|
syl2anc |
|
124 |
75
|
nn0red |
|
125 |
124
|
leidd |
|
126 |
109
|
expr |
|
127 |
126
|
ralrimiva |
|
128 |
|
breq1 |
|
129 |
|
fveq2 |
|
130 |
|
fveq2 |
|
131 |
129 130
|
sseq12d |
|
132 |
128 131
|
imbi12d |
|
133 |
132
|
rspcva |
|
134 |
75 127 133
|
syl2anc |
|
135 |
125 134
|
mpd |
|
136 |
135
|
adantr |
|
137 |
67
|
adantr |
|
138 |
70
|
adantr |
|
139 |
75
|
adantr |
|
140 |
|
simprl |
|
141 |
|
simprr |
|
142 |
1 10 11 137 138 139 140 141
|
hbtlem4 |
|
143 |
136 142
|
sstrd |
|
144 |
123 143
|
eqsstrd |
|
145 |
144
|
anassrs |
|
146 |
74 77 110 145
|
lecasei |
|
147 |
146
|
ralrimiva |
|
148 |
1 10 11 67 70 47 72 147
|
hbtlem5 |
|
149 |
148
|
eqcomd |
|
150 |
|
fveq2 |
|
151 |
150
|
rspceeqv |
|
152 |
66 149 151
|
syl2anc |
|
153 |
39 152
|
exlimddv |
|
154 |
25 153
|
rexlimddv |
|
155 |
154
|
ralrimiva |
|
156 |
48 10 27
|
islnr2 |
|
157 |
4 155 156
|
sylanbrc |
|