Step |
Hyp |
Ref |
Expression |
0 |
|
cuvc |
|- unitVec |
1 |
|
vr |
|- r |
2 |
|
cvv |
|- _V |
3 |
|
vi |
|- i |
4 |
|
vj |
|- j |
5 |
3
|
cv |
|- i |
6 |
|
vk |
|- k |
7 |
6
|
cv |
|- k |
8 |
4
|
cv |
|- j |
9 |
7 8
|
wceq |
|- k = j |
10 |
|
cur |
|- 1r |
11 |
1
|
cv |
|- r |
12 |
11 10
|
cfv |
|- ( 1r ` r ) |
13 |
|
c0g |
|- 0g |
14 |
11 13
|
cfv |
|- ( 0g ` r ) |
15 |
9 12 14
|
cif |
|- if ( k = j , ( 1r ` r ) , ( 0g ` r ) ) |
16 |
6 5 15
|
cmpt |
|- ( k e. i |-> if ( k = j , ( 1r ` r ) , ( 0g ` r ) ) ) |
17 |
4 5 16
|
cmpt |
|- ( j e. i |-> ( k e. i |-> if ( k = j , ( 1r ` r ) , ( 0g ` r ) ) ) ) |
18 |
1 3 2 2 17
|
cmpo |
|- ( r e. _V , i e. _V |-> ( j e. i |-> ( k e. i |-> if ( k = j , ( 1r ` r ) , ( 0g ` r ) ) ) ) ) |
19 |
0 18
|
wceq |
|- unitVec = ( r e. _V , i e. _V |-> ( j e. i |-> ( k e. i |-> if ( k = j , ( 1r ` r ) , ( 0g ` r ) ) ) ) ) |