Step |
Hyp |
Ref |
Expression |
1 |
|
minvec.x |
|
2 |
|
minvec.m |
|
3 |
|
minvec.n |
|
4 |
|
minvec.u |
|
5 |
|
minvec.y |
|
6 |
|
minvec.w |
|
7 |
|
minvec.a |
|
8 |
|
minvec.j |
|
9 |
|
minvec.r |
|
10 |
|
minvec.s |
|
11 |
|
minvec.d |
|
12 |
|
minvec.f |
|
13 |
|
minvec.p |
|
14 |
|
minvec.t |
|
15 |
1 2 3 4 5 6 7 8 9 10 11 12 13
|
minveclem4a |
|
16 |
15
|
elin2d |
|
17 |
11
|
oveqi |
|
18 |
1 2 3 4 5 6 7 8 9 10 11 12 13
|
minveclem4b |
|
19 |
7 18
|
ovresd |
|
20 |
17 19
|
syl5eq |
|
21 |
|
cphngp |
|
22 |
4 21
|
syl |
|
23 |
|
eqid |
|
24 |
3 1 2 23
|
ngpds |
|
25 |
22 7 18 24
|
syl3anc |
|
26 |
20 25
|
eqtrd |
|
27 |
26
|
adantr |
|
28 |
|
ngpms |
|
29 |
1 11
|
msmet |
|
30 |
22 28 29
|
3syl |
|
31 |
|
metcl |
|
32 |
30 7 18 31
|
syl3anc |
|
33 |
32
|
adantr |
|
34 |
1 2 3 4 5 6 7 8 9 10
|
minveclem4c |
|
35 |
34
|
adantr |
|
36 |
22
|
adantr |
|
37 |
|
cphlmod |
|
38 |
4 37
|
syl |
|
39 |
38
|
adantr |
|
40 |
7
|
adantr |
|
41 |
|
eqid |
|
42 |
1 41
|
lssss |
|
43 |
5 42
|
syl |
|
44 |
43
|
sselda |
|
45 |
1 2
|
lmodvsubcl |
|
46 |
39 40 44 45
|
syl3anc |
|
47 |
1 3
|
nmcl |
|
48 |
36 46 47
|
syl2anc |
|
49 |
34 32
|
ltnled |
|
50 |
1 2 3 4 5 6 7 8 9 10 11 12
|
minveclem3b |
|
51 |
|
fbsspw |
|
52 |
50 51
|
syl |
|
53 |
43
|
sspwd |
|
54 |
52 53
|
sstrd |
|
55 |
1
|
fvexi |
|
56 |
55
|
a1i |
|
57 |
|
fbasweak |
|
58 |
50 54 56 57
|
syl3anc |
|
59 |
58
|
adantr |
|
60 |
|
fgcl |
|
61 |
59 60
|
syl |
|
62 |
|
ssfg |
|
63 |
59 62
|
syl |
|
64 |
32 34
|
readdcld |
|
65 |
64
|
rehalfcld |
|
66 |
65
|
resqcld |
|
67 |
34
|
resqcld |
|
68 |
66 67
|
resubcld |
|
69 |
68
|
adantr |
|
70 |
34 32 34
|
ltadd1d |
|
71 |
34
|
recnd |
|
72 |
71
|
2timesd |
|
73 |
72
|
breq1d |
|
74 |
|
2re |
|
75 |
|
2pos |
|
76 |
74 75
|
pm3.2i |
|
77 |
76
|
a1i |
|
78 |
|
ltmuldiv2 |
|
79 |
34 64 77 78
|
syl3anc |
|
80 |
70 73 79
|
3bitr2d |
|
81 |
1 2 3 4 5 6 7 8 9
|
minveclem1 |
|
82 |
81
|
simp3d |
|
83 |
81
|
simp1d |
|
84 |
81
|
simp2d |
|
85 |
|
0re |
|
86 |
|
breq1 |
|
87 |
86
|
ralbidv |
|
88 |
87
|
rspcev |
|
89 |
85 82 88
|
sylancr |
|
90 |
85
|
a1i |
|
91 |
|
infregelb |
|
92 |
83 84 89 90 91
|
syl31anc |
|
93 |
82 92
|
mpbird |
|
94 |
93 10
|
breqtrrdi |
|
95 |
|
metge0 |
|
96 |
30 7 18 95
|
syl3anc |
|
97 |
32 34 96 94
|
addge0d |
|
98 |
|
divge0 |
|
99 |
64 97 77 98
|
syl21anc |
|
100 |
34 65 94 99
|
lt2sqd |
|
101 |
67 66
|
posdifd |
|
102 |
80 100 101
|
3bitrd |
|
103 |
102
|
biimpa |
|
104 |
69 103
|
elrpd |
|
105 |
14 104
|
eqeltrid |
|
106 |
5
|
adantr |
|
107 |
|
rabexg |
|
108 |
106 107
|
syl |
|
109 |
|
eqid |
|
110 |
|
oveq2 |
|
111 |
110
|
breq2d |
|
112 |
111
|
rabbidv |
|
113 |
109 112
|
elrnmpt1s |
|
114 |
105 108 113
|
syl2anc |
|
115 |
114 12
|
eleqtrrdi |
|
116 |
63 115
|
sseldd |
|
117 |
|
ssrab2 |
|
118 |
117
|
a1i |
|
119 |
14
|
oveq2i |
|
120 |
67
|
ad2antrr |
|
121 |
120
|
recnd |
|
122 |
65
|
ad2antrr |
|
123 |
122
|
resqcld |
|
124 |
123
|
recnd |
|
125 |
121 124
|
pncan3d |
|
126 |
119 125
|
syl5eq |
|
127 |
126
|
breq2d |
|
128 |
30
|
ad2antrr |
|
129 |
7
|
ad2antrr |
|
130 |
44
|
adantlr |
|
131 |
|
metcl |
|
132 |
128 129 130 131
|
syl3anc |
|
133 |
|
metge0 |
|
134 |
128 129 130 133
|
syl3anc |
|
135 |
99
|
ad2antrr |
|
136 |
132 122 134 135
|
le2sqd |
|
137 |
127 136
|
bitr4d |
|
138 |
137
|
rabbidva |
|
139 |
43
|
adantr |
|
140 |
|
rabss2 |
|
141 |
139 140
|
syl |
|
142 |
138 141
|
eqsstrd |
|
143 |
|
filss |
|
144 |
61 116 118 142 143
|
syl13anc |
|
145 |
|
flimclsi |
|
146 |
144 145
|
syl |
|
147 |
15
|
elin1d |
|
148 |
147
|
adantr |
|
149 |
146 148
|
sseldd |
|
150 |
|
ngpxms |
|
151 |
1 11
|
xmsxmet |
|
152 |
22 150 151
|
3syl |
|
153 |
152
|
adantr |
|
154 |
7
|
adantr |
|
155 |
65
|
adantr |
|
156 |
155
|
rexrd |
|
157 |
|
eqid |
|
158 |
|
eqid |
|
159 |
157 158
|
blcld |
|
160 |
153 154 156 159
|
syl3anc |
|
161 |
8 1 11
|
xmstopn |
|
162 |
22 150 161
|
3syl |
|
163 |
162
|
adantr |
|
164 |
163
|
fveq2d |
|
165 |
160 164
|
eleqtrrd |
|
166 |
|
cldcls |
|
167 |
165 166
|
syl |
|
168 |
149 167
|
eleqtrd |
|
169 |
|
oveq2 |
|
170 |
169
|
breq1d |
|
171 |
170
|
elrab |
|
172 |
171
|
simprbi |
|
173 |
168 172
|
syl |
|
174 |
32 34 32
|
leadd2d |
|
175 |
32
|
recnd |
|
176 |
175
|
2timesd |
|
177 |
176
|
breq1d |
|
178 |
|
lemuldiv2 |
|
179 |
76 178
|
mp3an3 |
|
180 |
32 64 179
|
syl2anc |
|
181 |
174 177 180
|
3bitr2d |
|
182 |
181
|
biimpar |
|
183 |
173 182
|
syldan |
|
184 |
183
|
ex |
|
185 |
49 184
|
sylbird |
|
186 |
185
|
pm2.18d |
|
187 |
186
|
adantr |
|
188 |
83
|
adantr |
|
189 |
89
|
adantr |
|
190 |
|
simpr |
|
191 |
|
fvex |
|
192 |
|
eqid |
|
193 |
192
|
elrnmpt1 |
|
194 |
190 191 193
|
sylancl |
|
195 |
194 9
|
eleqtrrdi |
|
196 |
|
infrelb |
|
197 |
188 189 195 196
|
syl3anc |
|
198 |
10 197
|
eqbrtrid |
|
199 |
33 35 48 187 198
|
letrd |
|
200 |
27 199
|
eqbrtrrd |
|
201 |
200
|
ralrimiva |
|
202 |
|
oveq2 |
|
203 |
202
|
fveq2d |
|
204 |
203
|
breq1d |
|
205 |
204
|
ralbidv |
|
206 |
205
|
rspcev |
|
207 |
16 201 206
|
syl2anc |
|