Description: Define the operation of vector addition. (Contributed by Andrew Salmon, 27-Jan-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | df-addr | |- +r = ( x e. _V , y e. _V |-> ( v e. RR |-> ( ( x ` v ) + ( y ` v ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cplusr | |- +r |
|
1 | vx | |- x |
|
2 | cvv | |- _V |
|
3 | vy | |- y |
|
4 | vv | |- v |
|
5 | cr | |- RR |
|
6 | 1 | cv | |- x |
7 | 4 | cv | |- v |
8 | 7 6 | cfv | |- ( x ` v ) |
9 | caddc | |- + |
|
10 | 3 | cv | |- y |
11 | 7 10 | cfv | |- ( y ` v ) |
12 | 8 11 9 | co | |- ( ( x ` v ) + ( y ` v ) ) |
13 | 4 5 12 | cmpt | |- ( v e. RR |-> ( ( x ` v ) + ( y ` v ) ) ) |
14 | 1 3 2 2 13 | cmpo | |- ( x e. _V , y e. _V |-> ( v e. RR |-> ( ( x ` v ) + ( y ` v ) ) ) ) |
15 | 0 14 | wceq | |- +r = ( x e. _V , y e. _V |-> ( v e. RR |-> ( ( x ` v ) + ( y ` v ) ) ) ) |