Step |
Hyp |
Ref |
Expression |
1 |
|
ballotth.m |
|
2 |
|
ballotth.n |
|
3 |
|
ballotth.o |
|
4 |
|
ballotth.p |
|
5 |
|
ballotth.f |
|
6 |
|
ballotth.e |
|
7 |
|
ballotth.mgtn |
|
8 |
|
ballotth.i |
|
9 |
|
eldifi |
|
10 |
9
|
ad2antrr |
|
11 |
1 2 3 4 5 6 7 8
|
ballotlemiex |
|
12 |
11
|
simpld |
|
13 |
|
elfznn |
|
14 |
12 13
|
syl |
|
15 |
14
|
adantr |
|
16 |
1 2 3 4 5 6 7 8
|
ballotlemi1 |
|
17 |
|
eluz2b3 |
|
18 |
15 16 17
|
sylanbrc |
|
19 |
|
uz2m1nn |
|
20 |
18 19
|
syl |
|
21 |
20
|
adantr |
|
22 |
|
elnnuz |
|
23 |
22
|
biimpi |
|
24 |
|
eluzfz1 |
|
25 |
20 23 24
|
3syl |
|
26 |
25
|
adantr |
|
27 |
|
1nn |
|
28 |
27
|
a1i |
|
29 |
1 2 3 4 5 9 28
|
ballotlemfp1 |
|
30 |
29
|
simpld |
|
31 |
30
|
imp |
|
32 |
|
1m1e0 |
|
33 |
32
|
fveq2i |
|
34 |
33
|
oveq1i |
|
35 |
34
|
a1i |
|
36 |
1 2 3 4 5
|
ballotlemfval0 |
|
37 |
9 36
|
syl |
|
38 |
37
|
adantr |
|
39 |
38
|
oveq1d |
|
40 |
31 35 39
|
3eqtrrd |
|
41 |
|
0le1 |
|
42 |
|
0re |
|
43 |
|
1re |
|
44 |
|
suble0 |
|
45 |
42 43 44
|
mp2an |
|
46 |
41 45
|
mpbir |
|
47 |
40 46
|
eqbrtrrdi |
|
48 |
47
|
adantr |
|
49 |
|
fveq2 |
|
50 |
49
|
breq1d |
|
51 |
50
|
rspcev |
|
52 |
26 48 51
|
syl2anc |
|
53 |
|
0lt1 |
|
54 |
|
1p0e1 |
|
55 |
1 2 3 4 5 9 14
|
ballotlemfp1 |
|
56 |
55
|
simpld |
|
57 |
56
|
imp |
|
58 |
11
|
simprd |
|
59 |
58
|
adantr |
|
60 |
57 59
|
eqtr3d |
|
61 |
9
|
adantr |
|
62 |
14
|
nnzd |
|
63 |
62
|
adantr |
|
64 |
|
1zzd |
|
65 |
63 64
|
zsubcld |
|
66 |
1 2 3 4 5 61 65
|
ballotlemfelz |
|
67 |
66
|
zcnd |
|
68 |
|
1cnd |
|
69 |
|
0cnd |
|
70 |
67 68 69
|
subaddd |
|
71 |
60 70
|
mpbid |
|
72 |
54 71
|
syl5eqr |
|
73 |
53 72
|
breqtrid |
|
74 |
73
|
adantlr |
|
75 |
1 2 3 4 5 10 21 52 74
|
ballotlemfc0 |
|
76 |
1 2 3 4 5 6 7 8
|
ballotlemimin |
|
77 |
76
|
ad2antrr |
|
78 |
75 77
|
condan |
|