Step |
Hyp |
Ref |
Expression |
1 |
|
gsumfsum.1 |
|
2 |
|
gsumfsum.2 |
|
3 |
|
mpteq1 |
|
4 |
|
mpt0 |
|
5 |
3 4
|
eqtrdi |
|
6 |
5
|
oveq2d |
|
7 |
|
cnfld0 |
|
8 |
7
|
gsum0 |
|
9 |
|
sum0 |
|
10 |
8 9
|
eqtr4i |
|
11 |
6 10
|
eqtrdi |
|
12 |
|
sumeq1 |
|
13 |
11 12
|
eqtr4d |
|
14 |
13
|
a1i |
|
15 |
|
cnfldbas |
|
16 |
|
cnfldadd |
|
17 |
|
eqid |
|
18 |
|
cnring |
|
19 |
|
ringmnd |
|
20 |
18 19
|
mp1i |
|
21 |
1
|
adantr |
|
22 |
2
|
fmpttd |
|
23 |
22
|
adantr |
|
24 |
|
ringcmn |
|
25 |
18 24
|
mp1i |
|
26 |
15 17 25 23
|
cntzcmnf |
|
27 |
|
simprl |
|
28 |
|
simprr |
|
29 |
|
f1of1 |
|
30 |
28 29
|
syl |
|
31 |
|
suppssdm |
|
32 |
31 23
|
fssdm |
|
33 |
|
f1ofo |
|
34 |
|
forn |
|
35 |
28 33 34
|
3syl |
|
36 |
32 35
|
sseqtrrd |
|
37 |
|
eqid |
|
38 |
15 7 16 17 20 21 23 26 27 30 36 37
|
gsumval3 |
|
39 |
|
sumfc |
|
40 |
|
fveq2 |
|
41 |
23
|
ffvelrnda |
|
42 |
|
f1of |
|
43 |
28 42
|
syl |
|
44 |
|
fvco3 |
|
45 |
43 44
|
sylan |
|
46 |
40 27 28 41 45
|
fsum |
|
47 |
39 46
|
syl5eqr |
|
48 |
38 47
|
eqtr4d |
|
49 |
48
|
expr |
|
50 |
49
|
exlimdv |
|
51 |
50
|
expimpd |
|
52 |
|
fz1f1o |
|
53 |
1 52
|
syl |
|
54 |
14 51 53
|
mpjaod |
|