Description: The difference of two group sums expressed as mappings. (Contributed by AV, 7-Nov-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | gsummptfssub.b | |
|
gsummptfssub.z | |
||
gsummptfssub.s | |
||
gsummptfssub.g | |
||
gsummptfssub.a | |
||
gsummptfssub.c | |
||
gsummptfssub.d | |
||
gsummptfssub.f | |
||
gsummptfssub.h | |
||
gsummptfssub.w | |
||
gsummptfssub.v | |
||
Assertion | gsummptfssub | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gsummptfssub.b | |
|
2 | gsummptfssub.z | |
|
3 | gsummptfssub.s | |
|
4 | gsummptfssub.g | |
|
5 | gsummptfssub.a | |
|
6 | gsummptfssub.c | |
|
7 | gsummptfssub.d | |
|
8 | gsummptfssub.f | |
|
9 | gsummptfssub.h | |
|
10 | gsummptfssub.w | |
|
11 | gsummptfssub.v | |
|
12 | 5 6 7 8 9 | offval2 | |
13 | 12 | eqcomd | |
14 | 13 | oveq2d | |
15 | 8 6 | fmpt3d | |
16 | 9 7 | fmpt3d | |
17 | 1 2 3 4 5 15 16 10 11 | gsumsub | |
18 | 14 17 | eqtrd | |