Step |
Hyp |
Ref |
Expression |
1 |
|
minveco.x |
|
2 |
|
minveco.m |
|
3 |
|
minveco.n |
|
4 |
|
minveco.y |
|
5 |
|
minveco.u |
|
6 |
|
minveco.w |
|
7 |
|
minveco.a |
|
8 |
|
minveco.d |
|
9 |
|
minveco.j |
|
10 |
|
minveco.r |
|
11 |
|
minveco.s |
|
12 |
|
nnrecgt0 |
|
13 |
12
|
adantl |
|
14 |
|
nnrecre |
|
15 |
14
|
adantl |
|
16 |
1 2 3 4 5 6 7 8 9 10
|
minvecolem1 |
|
17 |
16
|
adantr |
|
18 |
17
|
simp1d |
|
19 |
17
|
simp2d |
|
20 |
|
0re |
|
21 |
17
|
simp3d |
|
22 |
|
breq1 |
|
23 |
22
|
ralbidv |
|
24 |
23
|
rspcev |
|
25 |
20 21 24
|
sylancr |
|
26 |
|
infrecl |
|
27 |
18 19 25 26
|
syl3anc |
|
28 |
11 27
|
eqeltrid |
|
29 |
28
|
resqcld |
|
30 |
15 29
|
ltaddposd |
|
31 |
13 30
|
mpbid |
|
32 |
29 15
|
readdcld |
|
33 |
28
|
sqge0d |
|
34 |
29 15 33 13
|
addgegt0d |
|
35 |
32 34
|
elrpd |
|
36 |
35
|
rpge0d |
|
37 |
|
resqrtth |
|
38 |
32 36 37
|
syl2anc |
|
39 |
31 38
|
breqtrrd |
|
40 |
35
|
rpsqrtcld |
|
41 |
40
|
rpred |
|
42 |
|
0red |
|
43 |
|
infregelb |
|
44 |
18 19 25 42 43
|
syl31anc |
|
45 |
21 44
|
mpbird |
|
46 |
45 11
|
breqtrrdi |
|
47 |
32 36
|
sqrtge0d |
|
48 |
28 41 46 47
|
lt2sqd |
|
49 |
39 48
|
mpbird |
|
50 |
28 41
|
ltnled |
|
51 |
49 50
|
mpbid |
|
52 |
11
|
breq2i |
|
53 |
|
infregelb |
|
54 |
18 19 25 41 53
|
syl31anc |
|
55 |
52 54
|
syl5bb |
|
56 |
10
|
raleqi |
|
57 |
|
fvex |
|
58 |
57
|
rgenw |
|
59 |
|
eqid |
|
60 |
|
breq2 |
|
61 |
59 60
|
ralrnmptw |
|
62 |
58 61
|
ax-mp |
|
63 |
56 62
|
bitri |
|
64 |
55 63
|
bitrdi |
|
65 |
51 64
|
mtbid |
|
66 |
|
rexnal |
|
67 |
65 66
|
sylibr |
|
68 |
32
|
adantr |
|
69 |
|
phnv |
|
70 |
5 69
|
syl |
|
71 |
70
|
ad2antrr |
|
72 |
7
|
ad2antrr |
|
73 |
|
inss1 |
|
74 |
73 6
|
sseldi |
|
75 |
|
eqid |
|
76 |
1 4 75
|
sspba |
|
77 |
70 74 76
|
syl2anc |
|
78 |
77
|
adantr |
|
79 |
78
|
sselda |
|
80 |
1 2
|
nvmcl |
|
81 |
71 72 79 80
|
syl3anc |
|
82 |
1 3
|
nvcl |
|
83 |
71 81 82
|
syl2anc |
|
84 |
83
|
resqcld |
|
85 |
68 84
|
letrid |
|
86 |
85
|
ord |
|
87 |
41
|
adantr |
|
88 |
47
|
adantr |
|
89 |
1 3
|
nvge0 |
|
90 |
71 81 89
|
syl2anc |
|
91 |
87 83 88 90
|
le2sqd |
|
92 |
38
|
adantr |
|
93 |
92
|
breq1d |
|
94 |
91 93
|
bitrd |
|
95 |
94
|
notbid |
|
96 |
1 2 3 8
|
imsdval |
|
97 |
71 72 79 96
|
syl3anc |
|
98 |
97
|
oveq1d |
|
99 |
98
|
breq1d |
|
100 |
86 95 99
|
3imtr4d |
|
101 |
100
|
reximdva |
|
102 |
67 101
|
mpd |
|
103 |
102
|
ralrimiva |
|
104 |
4
|
fvexi |
|
105 |
|
nnenom |
|
106 |
|
oveq2 |
|
107 |
106
|
oveq1d |
|
108 |
107
|
breq1d |
|
109 |
104 105 108
|
axcc4 |
|
110 |
103 109
|
syl |
|
111 |
5
|
adantr |
|
112 |
6
|
adantr |
|
113 |
7
|
adantr |
|
114 |
|
simprl |
|
115 |
|
simprr |
|
116 |
|
fveq2 |
|
117 |
116
|
oveq2d |
|
118 |
117
|
oveq1d |
|
119 |
|
oveq2 |
|
120 |
119
|
oveq2d |
|
121 |
118 120
|
breq12d |
|
122 |
121
|
rspccva |
|
123 |
115 122
|
sylan |
|
124 |
|
eqid |
|
125 |
1 2 3 4 111 112 113 8 9 10 11 114 123 124
|
minvecolem4 |
|
126 |
110 125
|
exlimddv |
|