Step |
Hyp |
Ref |
Expression |
1 |
|
fmul01lt1lem1.1 |
|
2 |
|
fmul01lt1lem1.2 |
|
3 |
|
fmul01lt1lem1.3 |
|
4 |
|
fmul01lt1lem1.4 |
|
5 |
|
fmul01lt1lem1.5 |
|
6 |
|
fmul01lt1lem1.6 |
|
7 |
|
fmul01lt1lem1.7 |
|
8 |
|
fmul01lt1lem1.8 |
|
9 |
|
fmul01lt1lem1.9 |
|
10 |
|
fmul01lt1lem1.10 |
|
11 |
|
simpr |
|
12 |
11
|
fveq2d |
|
13 |
3
|
a1i |
|
14 |
13
|
fveq1d |
|
15 |
|
seq1 |
|
16 |
4 15
|
syl |
|
17 |
16
|
adantr |
|
18 |
12 14 17
|
3eqtrd |
|
19 |
10
|
adantr |
|
20 |
18 19
|
eqbrtrd |
|
21 |
|
simpr |
|
22 |
21
|
neqned |
|
23 |
4
|
zred |
|
24 |
|
eluzelz |
|
25 |
5 24
|
syl |
|
26 |
25
|
zred |
|
27 |
|
eluzle |
|
28 |
5 27
|
syl |
|
29 |
23 26 28
|
3jca |
|
30 |
29
|
adantr |
|
31 |
|
leltne |
|
32 |
30 31
|
syl |
|
33 |
22 32
|
mpbird |
|
34 |
3
|
fveq1i |
|
35 |
|
remulcl |
|
36 |
35
|
adantl |
|
37 |
|
recn |
|
38 |
37
|
3ad2ant1 |
|
39 |
|
recn |
|
40 |
39
|
3ad2ant2 |
|
41 |
|
recn |
|
42 |
41
|
3ad2ant3 |
|
43 |
38 40 42
|
mulassd |
|
44 |
43
|
adantl |
|
45 |
|
simpr |
|
46 |
45
|
olcd |
|
47 |
26 23
|
jca |
|
48 |
47
|
adantr |
|
49 |
|
lttri2 |
|
50 |
48 49
|
syl |
|
51 |
46 50
|
mpbird |
|
52 |
51
|
neneqd |
|
53 |
|
uzp1 |
|
54 |
5 53
|
syl |
|
55 |
54
|
adantr |
|
56 |
55
|
ord |
|
57 |
52 56
|
mpd |
|
58 |
4
|
adantr |
|
59 |
|
uzid |
|
60 |
58 59
|
syl |
|
61 |
|
nfv |
|
62 |
2 61
|
nfan |
|
63 |
|
nfcv |
|
64 |
1 63
|
nffv |
|
65 |
64
|
nfel1 |
|
66 |
62 65
|
nfim |
|
67 |
|
eleq1 |
|
68 |
67
|
anbi2d |
|
69 |
|
fveq2 |
|
70 |
69
|
eleq1d |
|
71 |
68 70
|
imbi12d |
|
72 |
66 71 6
|
chvarfv |
|
73 |
72
|
adantlr |
|
74 |
36 44 57 60 73
|
seqsplit |
|
75 |
|
eluzfz1 |
|
76 |
5 75
|
syl |
|
77 |
76
|
ancli |
|
78 |
|
nfv |
|
79 |
2 78
|
nfan |
|
80 |
|
nfcv |
|
81 |
1 80
|
nffv |
|
82 |
81
|
nfel1 |
|
83 |
79 82
|
nfim |
|
84 |
|
eleq1 |
|
85 |
84
|
anbi2d |
|
86 |
|
fveq2 |
|
87 |
86
|
eleq1d |
|
88 |
85 87
|
imbi12d |
|
89 |
83 88 6
|
vtoclg1f |
|
90 |
76 77 89
|
sylc |
|
91 |
16 90
|
eqeltrd |
|
92 |
91
|
adantr |
|
93 |
4
|
adantr |
|
94 |
25
|
adantr |
|
95 |
|
elfzelz |
|
96 |
95
|
adantl |
|
97 |
93 94 96
|
3jca |
|
98 |
23
|
adantr |
|
99 |
|
peano2re |
|
100 |
23 99
|
syl |
|
101 |
100
|
adantr |
|
102 |
95
|
zred |
|
103 |
102
|
adantl |
|
104 |
23
|
lep1d |
|
105 |
104
|
adantr |
|
106 |
|
elfzle1 |
|
107 |
106
|
adantl |
|
108 |
98 101 103 105 107
|
letrd |
|
109 |
|
elfzle2 |
|
110 |
109
|
adantl |
|
111 |
108 110
|
jca |
|
112 |
|
elfz2 |
|
113 |
97 111 112
|
sylanbrc |
|
114 |
113 72
|
syldan |
|
115 |
114
|
adantlr |
|
116 |
57 115 36
|
seqcl |
|
117 |
92 116
|
remulcld |
|
118 |
9
|
rpred |
|
119 |
118
|
adantr |
|
120 |
|
1red |
|
121 |
|
nfcv |
|
122 |
|
nfcv |
|
123 |
121 122 81
|
nfbr |
|
124 |
79 123
|
nfim |
|
125 |
86
|
breq2d |
|
126 |
85 125
|
imbi12d |
|
127 |
124 126 7
|
vtoclg1f |
|
128 |
76 77 127
|
sylc |
|
129 |
128 16
|
breqtrrd |
|
130 |
129
|
adantr |
|
131 |
|
nfv |
|
132 |
2 131
|
nfan |
|
133 |
|
eqid |
|
134 |
4
|
peano2zd |
|
135 |
134
|
adantr |
|
136 |
23
|
adantr |
|
137 |
136 45
|
gtned |
|
138 |
137
|
neneqd |
|
139 |
5
|
adantr |
|
140 |
139 53
|
syl |
|
141 |
|
orel1 |
|
142 |
138 140 141
|
sylc |
|
143 |
25
|
adantr |
|
144 |
135 143 143
|
3jca |
|
145 |
|
zltp1le |
|
146 |
58 143 145
|
syl2anc |
|
147 |
45 146
|
mpbid |
|
148 |
26
|
adantr |
|
149 |
148
|
leidd |
|
150 |
147 149
|
jca |
|
151 |
|
elfz2 |
|
152 |
144 150 151
|
sylanbrc |
|
153 |
4
|
adantr |
|
154 |
25
|
adantr |
|
155 |
|
elfzelz |
|
156 |
155
|
adantl |
|
157 |
153 154 156
|
3jca |
|
158 |
23
|
adantr |
|
159 |
158 99
|
syl |
|
160 |
155
|
zred |
|
161 |
160
|
adantl |
|
162 |
104
|
adantr |
|
163 |
|
elfzle1 |
|
164 |
163
|
adantl |
|
165 |
158 159 161 162 164
|
letrd |
|
166 |
|
elfzle2 |
|
167 |
166
|
adantl |
|
168 |
165 167
|
jca |
|
169 |
|
elfz2 |
|
170 |
157 168 169
|
sylanbrc |
|
171 |
170 6
|
syldan |
|
172 |
171
|
adantlr |
|
173 |
|
simpll |
|
174 |
4
|
ad2antrr |
|
175 |
25
|
ad2antrr |
|
176 |
155
|
adantl |
|
177 |
174 175 176
|
3jca |
|
178 |
23
|
ad2antrr |
|
179 |
100
|
ad2antrr |
|
180 |
160
|
adantl |
|
181 |
104
|
ad2antrr |
|
182 |
163
|
adantl |
|
183 |
178 179 180 181 182
|
letrd |
|
184 |
166
|
adantl |
|
185 |
183 184
|
jca |
|
186 |
177 185 169
|
sylanbrc |
|
187 |
173 186 7
|
syl2anc |
|
188 |
173 186 8
|
syl2anc |
|
189 |
1 132 133 135 142 152 172 187 188
|
fmul01 |
|
190 |
189
|
simprd |
|
191 |
116 120 92 130 190
|
lemul2ad |
|
192 |
91
|
recnd |
|
193 |
192
|
mulid1d |
|
194 |
193
|
adantr |
|
195 |
191 194
|
breqtrd |
|
196 |
16 10
|
eqbrtrd |
|
197 |
196
|
adantr |
|
198 |
117 92 119 195 197
|
lelttrd |
|
199 |
74 198
|
eqbrtrd |
|
200 |
34 199
|
eqbrtrid |
|
201 |
33 200
|
syldan |
|
202 |
20 201
|
pm2.61dan |
|