Step |
Hyp |
Ref |
Expression |
1 |
|
sumsplit.1 |
|
2 |
|
sumsplit.2 |
|
3 |
|
sumsplit.3 |
|
4 |
|
sumsplit.4 |
|
5 |
|
sumsplit.5 |
|
6 |
|
sumsplit.6 |
|
7 |
|
sumsplit.7 |
|
8 |
|
sumsplit.8 |
|
9 |
|
sumsplit.9 |
|
10 |
7
|
ralrimiva |
|
11 |
1
|
eqimssi |
|
12 |
11
|
a1i |
|
13 |
12
|
orcd |
|
14 |
|
sumss2 |
|
15 |
4 10 13 14
|
syl21anc |
|
16 |
|
iftrue |
|
17 |
16
|
adantl |
|
18 |
|
elun1 |
|
19 |
18 7
|
sylan2 |
|
20 |
17 19
|
eqeltrd |
|
21 |
|
iffalse |
|
22 |
|
0cn |
|
23 |
21 22
|
eqeltrdi |
|
24 |
23
|
adantl |
|
25 |
20 24
|
pm2.61dan |
|
26 |
25
|
adantr |
|
27 |
|
iftrue |
|
28 |
27
|
adantl |
|
29 |
|
elun2 |
|
30 |
29 7
|
sylan2 |
|
31 |
28 30
|
eqeltrd |
|
32 |
|
iffalse |
|
33 |
32 22
|
eqeltrdi |
|
34 |
33
|
adantl |
|
35 |
31 34
|
pm2.61dan |
|
36 |
35
|
adantr |
|
37 |
1 2 5 26 6 36 8 9
|
isumadd |
|
38 |
19
|
addid1d |
|
39 |
|
noel |
|
40 |
3
|
eleq2d |
|
41 |
|
elin |
|
42 |
40 41
|
bitr3di |
|
43 |
39 42
|
mtbii |
|
44 |
|
imnan |
|
45 |
43 44
|
sylibr |
|
46 |
45
|
imp |
|
47 |
46 32
|
syl |
|
48 |
17 47
|
oveq12d |
|
49 |
|
iftrue |
|
50 |
18 49
|
syl |
|
51 |
50
|
adantl |
|
52 |
38 48 51
|
3eqtr4rd |
|
53 |
35
|
addid2d |
|
54 |
53
|
adantr |
|
55 |
21
|
adantl |
|
56 |
55
|
oveq1d |
|
57 |
|
elun |
|
58 |
|
biorf |
|
59 |
57 58
|
bitr4id |
|
60 |
59
|
adantl |
|
61 |
60
|
ifbid |
|
62 |
54 56 61
|
3eqtr4rd |
|
63 |
52 62
|
pm2.61dan |
|
64 |
63
|
sumeq2sdv |
|
65 |
4
|
unssad |
|
66 |
19
|
ralrimiva |
|
67 |
|
sumss2 |
|
68 |
65 66 13 67
|
syl21anc |
|
69 |
4
|
unssbd |
|
70 |
30
|
ralrimiva |
|
71 |
|
sumss2 |
|
72 |
69 70 13 71
|
syl21anc |
|
73 |
68 72
|
oveq12d |
|
74 |
37 64 73
|
3eqtr4rd |
|
75 |
15 74
|
eqtr4d |
|